Maths-
General
Easy

Question

The number of values of c such that st. line y = 4x + c touches the curve fraction numerator x to the power of 2 end exponent over denominator 4 end fraction plus y to the power of 2 end exponent equals 1 is

  1. 0    
  2. 1    
  3. 2    
  4. infinite.    

hintHint:

Equation of ellipse =
x squared over a squared space plus y squared over b squared space equals 1

The correct answer is: 2



    Equation of ellipse = x squared over a squared space plus y squared over b squared space equals 1
    x squared over 2 squared space plus space y squared over 1 squared space equals 1, a = 2 and b = 1
    Given : straight line equation =  y = 4x + c , where m = 4
    We know that
    General equation of tangent of ellipse (y) = m x space plus-or-minus square root of a squared m squared plus b squared end root
    Substituting the values in above equation
    y = 4 x space plus-or-minus space square root of 2 squared 4 to the power of 2 space end exponent plus 1 squared end root
    y = 4 x space plus-or-minus space square root of 65
 comparing with y = 4x + c rightwards double arrow space c space equals plus-or-minus 65
    Thus, we have 2 values of c i.e. plus-or-minus 65

    Related Questions to study

    General
    Maths-

    Tangents are drawn to the ellipse fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 5 end fraction equals 1 at the ends of the latus rectum. The are of the quadrilateral so formed is

    Tangents are drawn to the ellipse fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 5 end fraction equals 1 at the ends of the latus rectum. The are of the quadrilateral so formed is

    Maths-General
    General
    Maths-

    A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x2 + 2y2 = 6 is

    A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x2 + 2y2 = 6 is

    Maths-General
    General
    physics

    Here are the graphs of x→ t of moving body. which of them is not suitable?

    Here are the graphs of x→ t of moving body. which of them is not suitable?

    physicsGeneral
    parallel
    General
    Maths-

    A cubic polynomial f(x) = ax3 + bx2 + cx + d has a graph which touches the x-axis at 2, has another x-intercept at –1 and has y-intercept at –2 as shown. The value of, a + b + c + d equals

    I f space a space f u n c t i o n space h a s space a space tan g e n t space a t space a space p o i n t space x equals a space comma space t h e n comma space i t space m e a n s comma space i t space i s space t h e space c r i t i c a l space p o i n t space o f space t h a t space f u n c t i o n space a n d space t h e space d e r i v a t i v e space o f space t h e space f u n c t i o n space i s space z e r o space a t space t h a t space p o i n t. space
P e r f o r m space t h e space c a l c u l a t i o n s space c a r e f u l l y comma space t o space a v o i d space s i l l y space m i s t a k e s.
space O n e space s h o u l d space k n o w space h o w space t o space r e a d space a space g r a p h space t o space s o l v e space s u c h space q u e s t i o n s.

    A cubic polynomial f(x) = ax3 + bx2 + cx + d has a graph which touches the x-axis at 2, has another x-intercept at –1 and has y-intercept at –2 as shown. The value of, a + b + c + d equals

    Maths-General

    I f space a space f u n c t i o n space h a s space a space tan g e n t space a t space a space p o i n t space x equals a space comma space t h e n comma space i t space m e a n s comma space i t space i s space t h e space c r i t i c a l space p o i n t space o f space t h a t space f u n c t i o n space a n d space t h e space d e r i v a t i v e space o f space t h e space f u n c t i o n space i s space z e r o space a t space t h a t space p o i n t. space
P e r f o r m space t h e space c a l c u l a t i o n s space c a r e f u l l y comma space t o space a v o i d space s i l l y space m i s t a k e s.
space O n e space s h o u l d space k n o w space h o w space t o space r e a d space a space g r a p h space t o space s o l v e space s u c h space q u e s t i o n s.

    General
    Maths-

    Consider f(x) = |1–x| 1 £ x £ 2 and g(x )= f(x) + b sin invisible function application fraction numerator pi over denominator 2 end fraction x, 1 £ x £ 2 then which of the following is correct?

    Consider f(x) = |1–x| 1 £ x £ 2 and g(x )= f(x) + b sin invisible function application fraction numerator pi over denominator 2 end fraction x, 1 £ x £ 2 then which of the following is correct?

    Maths-General
    General
    Maths-

    The value of c in Lagrange’s theorem for the function f(x) = log sin x in the interval open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator 5 pi over denominator 6 end fraction close square bracketsis -

    The value of c in Lagrange’s theorem for the function f(x) = log sin x in the interval open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator 5 pi over denominator 6 end fraction close square bracketsis -

    Maths-General
    parallel
    General
    physics

    The relation between time and displacement of a moving particle is given by t equals 2 a x squaredwhere alpha is a constant. The shape of the graph  is x not stretchy rightwards arrow y is....

    The relation between time and displacement of a moving particle is given by t equals 2 a x squaredwhere alpha is a constant. The shape of the graph  is x not stretchy rightwards arrow y is....

    physicsGeneral
    General
    Maths-

    If P (q) and Q open parentheses fraction numerator pi over denominator 2 end fraction plus theta close parentheses are two points on the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1, then locus of the mid – point of PQ is

    If P (q) and Q open parentheses fraction numerator pi over denominator 2 end fraction plus theta close parentheses are two points on the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1, then locus of the mid – point of PQ is

    Maths-General
    General
    Maths-

    If CP and CD are semi – conjugate diameters of an ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 comma then CP2 + CD2 =

    If CP and CD are semi – conjugate diameters of an ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 comma then CP2 + CD2 =

    Maths-General
    parallel
    General
    Maths-

    The normals to the curve x = a (theta + sin theta), y = a (1 – cos theta) at the points theta = (2n + 1) pi, n element of I are all -

    The normals to the curve x = a (theta + sin theta), y = a (1 – cos theta) at the points theta = (2n + 1) pi, n element of I are all -

    Maths-General
    General
    Maths-

    The normal to the curve x = 3 cos thetacos cubed theta, y = 3 sin thetasin cubedtheta at the point theta = pi/4 passes through the point -

    The normal to the curve x = 3 cos thetacos cubed theta, y = 3 sin thetasin cubedtheta at the point theta = pi/4 passes through the point -

    Maths-General
    General
    Maths-

    The normal of the curve given by the equation x = a (sintheta + costheta), y = a (sintheta – costheta) at the point Q is -

    The normal of the curve given by the equation x = a (sintheta + costheta), y = a (sintheta – costheta) at the point Q is -

    Maths-General
    parallel
    General
    Maths-

    If the tangent at ‘t’ on the curve y = 8 t cubed space minus 1x = 4 t squared space plus space 3 meets the curve again at t subscript 1 and is normal to the curve at that point, then value of t must be -

    If the tangent at ‘t’ on the curve y = 8 t cubed space minus 1x = 4 t squared space plus space 3 meets the curve again at t subscript 1 and is normal to the curve at that point, then value of t must be -

    Maths-General
    General
    Maths-

    The tangent at (t, t squared – t cubed) on the curve y = x squared – x cubed meets the curve again at Q, then abscissa of Q must be -

    The tangent at (t, t squared – t cubed) on the curve y = x squared – x cubed meets the curve again at Q, then abscissa of Q must be -

    Maths-General
    General
    Maths-

    If fraction numerator x over denominator a end fraction plus fraction numerator y over denominator b end fraction = 1 is a tangent to the curve x = 4t,y =fraction numerator 4 over denominator t end fraction, t element of R then -

    If fraction numerator x over denominator a end fraction plus fraction numerator y over denominator b end fraction = 1 is a tangent to the curve x = 4t,y =fraction numerator 4 over denominator t end fraction, t element of R then -

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.