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Maths-

General

Easy

Question

If the parabola y² = 4ax passes through (3, 2), then length of latus rectum of the parabola is

$\frac{2}{3}$
$\frac{4}{3}$
$\frac{1}{3}$
4

The correct answer is: $fraction numerator 4 over denominator 3 end fraction$

We have 4 = 4a × 3
LSL' = 4a = $fraction numerator 4 over denominator 3 end fraction$

Related Questions to study

The locus of the poles of focal chord of the parabola y² = 4ax is

The locus of the poles of focal chord of the parabola y² = 4ax is

The locus of the mid points of the chords of the parabola y² = 4ax which passes through a given point (β, $proportional to$ )

The locus of the mid points of the chords of the parabola y² = 4ax which passes through a given point (β, $proportional to$ )

The equation of common tangent to the curves y² = 8x and xy = –1 is

The equation of common tangent to the curves y² = 8x and xy = –1 is

parallel

Angle between tangents drawn from the point (1, 4) to the parabola y² = 4x is

Angle between tangents drawn from the point (1, 4) to the parabola y² = 4x is

The general equation of 2nd degree 9x² –24xy + 16y² – 20x –15y – 60 = 0 represents

The general equation of 2nd degree 9x² –24xy + 16y² – 20x –15y – 60 = 0 represents

If (2, 0) is the vertex and y-axis is the directrix of the parabola then its focus is

If (2, 0) is the vertex and y-axis is the directrix of the parabola then its focus is

parallel

The equation of directrix of the parabola y² + 4y + 4x + 2 = 0 is

The equation of directrix of the parabola y² + 4y + 4x + 2 = 0 is

The parametric representation of a parabola is x = 3 + t², y = 2t – 1. Its focus is -

The parametric representation of a parabola is x = 3 + t², y = 2t – 1. Its focus is -

A disc of mass 2 M and radius R is placed on a fixed plank (rough) of length L. The coefficient of friction between the plank and disc is $mu$ = 0.5. String (light) is connected to centre of disc and passing over a smooth light pulley and connected to a block of mass M as shown in the figure. Now the disc is given an angular velocity $omega subscript 0 end subscript$ in clockwise direction and is gently placed on the plank. Consider this instant as t=0. Based on above information, answer the following questions : Mark the correct statement w.r.t. motion of block and disc.

A disc of mass 2 M and radius R is placed on a fixed plank (rough) of length L. The coefficient of friction between the plank and disc is $mu$ = 0.5. String (light) is connected to centre of disc and passing over a smooth light pulley and connected to a block of mass M as shown in the figure. Now the disc is given an angular velocity $omega subscript 0 end subscript$ in clockwise direction and is gently placed on the plank. Consider this instant as t=0. Based on above information, answer the following questions : Mark the correct statement w.r.t. motion of block and disc.

physics-General

parallel

The locus of the point of intersection of the tangents to the parabola x² – 4x – 8y + 28 = 0 which are at right angle is -

The locus of the point of intersection of the tangents to the parabola x² – 4x – 8y + 28 = 0 which are at right angle is -

An equilateral triangle is inscribed in the parabola y² = 4ax whose vertices are at the parabola, then the length of its side is equal to -

An equilateral triangle is inscribed in the parabola y² = 4ax whose vertices are at the parabola, then the length of its side is equal to -

If the tangent to the parabola y² = ax makes an angle of 45º with x-axis, then the point of contact is

If the tangent to the parabola y² = ax makes an angle of 45º with x-axis, then the point of contact is

parallel

Two perpendicular tangents to y² = 4ax always intersect on the line, if

Two perpendicular tangents to y² = 4ax always intersect on the line, if

The equation of the tangent to the parabola y² = 4ax at point (a/t², 2a/t) is

The equation of the tangent to the parabola y² = 4ax at point (a/t², 2a/t) is

The line $ell$ x + my + n = 0 will touch the parabola y² = 4ax, if

The line $ell$ x + my + n = 0 will touch the parabola y² = 4ax, if

parallel

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