Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

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

y = 0
y = – 1
x = 1
y = 1

The correct answer is: y = 1

x² – 4x – 8y + 28 = 0
locus of pt of intersection of $perpendicular$ tangents is directrix
x² – 4x + 4 = 8y – 28 + 4 $rightwards double arrow$ (x – 2)² = 8y – 24
(x – 2)² = 8(y – 3) $rightwards double arrow$ X² = 8Y
equation of directrix
Y = – 2 $rightwards double arrow$ y – 3 = – 2 $rightwards double arrow$ y = 1

Related Questions to study

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

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

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

parallel

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

If y₁, y₂ are the ordinates of two points P and Q on the parabola and y₃ is the ordinate of the point of intersection of tangents at P and Q, then

If y₁, y₂ are the ordinates of two points P and Q on the parabola and y₃ is the ordinate of the point of intersection of tangents at P and Q, then

parallel

The line y = 2x + c is a tangent to the parabola y² = 16 x, if c equals

The line y = 2x + c is a tangent to the parabola y² = 16 x, if c equals

The straight line y = 2x + $lambda$ does not meet the parabola y² = 2x, if

The straight line y = 2x + $lambda$ does not meet the parabola y² = 2x, if

The equation of the tangent to the parabola y = x² – x at the point where x = 1, is

The equation of the tangent to the parabola y = x² – x at the point where x = 1, is

parallel

If line 2x + y + λ = 0 is normal to y² = 8x than λ =

If line 2x + y + λ = 0 is normal to y² = 8x than λ =

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: Time $t subscript 0 end subscript$ up to which the block remains stationary 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: Time $t subscript 0 end subscript$ up to which the block remains stationary is

physics-General

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: Time $t subscript 0 end subscript$ 1 at which the disc will cross the other end of the plank 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: Time $t subscript 0 end subscript$ 1 at which the disc will cross the other end of the plank is-

physics-General

parallel

A hollow sphere is released from the top of a wedge, friction is sufficient for pure rolling of sphere on the wedge. There is no friction between the wedge and the ground. Radius of sphere is R. At the instant it leaves the wedge horizontally. Velocity of centre of mass of sphere w.r.t. ground is-

A hollow sphere is released from the top of a wedge, friction is sufficient for pure rolling of sphere on the wedge. There is no friction between the wedge and the ground. Radius of sphere is R. At the instant it leaves the wedge horizontally. Velocity of centre of mass of sphere w.r.t. ground is-

physics-General

A hollow sphere is released from the top of a wedge, friction is sufficient for pure rolling of sphere on the wedge. There is no friction between the wedge and the ground. Radius of sphere is R. At the instant it leaves the wedge horizontally. Angular velocity of sphere $omega$ is

A hollow sphere is released from the top of a wedge, friction is sufficient for pure rolling of sphere on the wedge. There is no friction between the wedge and the ground. Radius of sphere is R. At the instant it leaves the wedge horizontally. Angular velocity of sphere $omega$ is

physics-General

A uniform hollow sphere is released from the top of a fixed inclined plane of inclination $37 to the power of ring operator end exponent$ and height 3m. It rolls without sliding. The time taken by the sphere to reach the bottom is

A uniform hollow sphere is released from the top of a fixed inclined plane of inclination $37 to the power of ring operator end exponent$ and height 3m. It rolls without sliding. The time taken by the sphere to reach the bottom is

physics-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.