The tangent at any point on the curve x=...

The tangent at any point on the curve `x=acos^3theta,y=asin^3theta` meets the axes in `Pa n dQ` . Prove that the locus of the midpoint of `P Q` is a circle.

Text Solution

AI Generated Solution

Topper's Solved these Questions

APPLICATION OF DERIVATIVES
CENGAGE ENGLISH|Exercise SOLVED EXAMPLES|15 Videos
APPLICATION OF DERIVATIVES
CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|3 Videos
APPLICATION OF DERIVATIVES
CENGAGE ENGLISH|Exercise JEE PREVIOUS YEAR|10 Videos
3D COORDINATION SYSTEM
CENGAGE ENGLISH|Exercise DPP 3.1|11 Videos
APPLICATION OF INTEGRALS
CENGAGE ENGLISH|Exercise All Questions|142 Videos

Similar Questions

Explore conceptually related problems

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at A and B . Then find the locus of the midpoint of A Bdot

If x=acos^3theta,y=a sin^3theta then find (d^2y)/(dx^(2))

Find the slope of the normal to the curve x=a\ cos^3theta , y=a\ sin^3theta at theta=pi/4 .

x=acos^(3)theta,y=asin^(3)theta then find (d^(2)y)/(dx^(2))

The tangent at any point P on the circle x^2 + y^2 = 2 cuts the axes in L and M . Find the locus of the middle point of LM .

If a tangent to the circle x^(2)+y^(2)=1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is :

If x=acos^3theta,y=a sin^3theta, then find the value of d2y/dx2 at θ=π/6

The tangent at any point P on y^2 = 4x meets x-axis at Q, then locus of mid point of PQ will be

A point P(x , y) moves in the xy-plane such that x=acos^2theta and y=2asintheta, where theta is a parameter. The locus of the point P is a/an circle (b) aellipse unbounded parabola (d) part of the parabola

The tangent drawn at any point of the curve sqrtx+sqrty = sqrta meets the OX and OY axes at points P and Q respectively, prove that OP+OQ = a.

CENGAGE ENGLISH-APPLICATION OF DERIVATIVES-ILLUSTRATION

about to only mathematics
Text Solution
|
Prove that points of the curve y^2=4a{x+asin(x/a)} at which tangents a...
Text Solution
|
The tangent at any point on the curve x=acos^3theta,y=asin^3theta meet...
Text Solution
|
Displacement s of a particle at time t is expressed as s=1/2t^3-6tdot ...
Text Solution
|
On the curve x^3=12 y , find the interval of values of x for which the...
Text Solution
|
एक आयत की लम्बाई x, 5 cm / min की दर से घट रही है और चौड़ाई y, 4 cm / ...
Text Solution
|
Let x be the length of one of the equal sides of an isosceles triangle...
Text Solution
|
A lamp is 50ftdot above the ground. A ball is dropped from the same he...
Text Solution
|
If water is poured into an inverted hollow cone whose semi-vertical ...
Text Solution
|
A horse runs along a circle with a speed of 20k m//h . A lantern is at...
Text Solution
|
A ladder 5 m long is leaning against a wall. The bottom of the ladder ...
Text Solution
|
The radius of the base of a cone is increasing at the rate of 3 cm/min...
Text Solution
|
Use differential to approximate sqrt(36. 6)
Text Solution
|
Find the approximate value of sin 3.
Text Solution
|
Find the approximate volume of metal in a hollow spherical shell wh...
Text Solution
|
Find the approximate value of f(5. 001), where f(x)=x^3-7x^2+15.
Text Solution
|
Find the approximate change in the volume V of a cube of side x meters...
Text Solution
|
Discuss the applicability of Rolles theorem for the following funct...
Text Solution
|
If the function f(x)=x^3-6x^2+a x+b defined on [1,3] satisfies Rolles ...
Text Solution
|
Show that between any two roots of e^(-x)-cosx=0, there exists at leas...
Text Solution
|