Home
Class 12
MATHS
Coordinates of points on curve 5x^(2) - ...

Coordinates of points on curve `5x^(2) - 6xy +5y^(2) - 4 = 0` which are nearest to origin are

A

`((1)/(2),(1)/(2))`

B

`(-(1)/(2),(1)/(2))`

C

`(-(1)/(2),-(1)/(2))`

D

`((1)/(2),-(1)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
B, D
Put `x = r cos theta,y = r sin theta` in given equation
`5r^(2) - 3r^(2) sin 2 theta = 4`
`rArr r^(2) =(4)/(5-3 sin 2theta)`
`rArr r_(min)^(2) = 4//8 = 1//2` (when `sin 2 theta =- 1)`
`rArr r_(min) = (1)/(sqrt(2))` at `2 theta =(3pi)/(2),(7pi)/(2)`, as `[2theta in (0,4pi)]`
So `theta = (3pi)/(4),(7pi)/(4)`
So points are `((1)/(sqrt(2))cos theta,(1)/(sqrt(2))sin theta)`
`= (-(1)/(2),(1)/(2))` and `((1)/(2),-(1)/(2))`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSTEM

    CENGAGE|Exercise Comprehension Type|4 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CENGAGE|Exercise Question Bank|1 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise JEE Main Previous Year|6 Videos

Similar Questions

Explore conceptually related problems

Find the points on the curve y^(2) - 4xy = x^(2) + 5 for which the tangent is horizontal.

The point on the curve x^(2) = 2y which is nearest to the point (0, 5) is

The point of curve y= 2x^(2) - 6x -4 at which the tangent is parallel to x-axis is

Find the points on the curve y^(2)-4xy=x^(2)+5 for which the tangent is horizontal.

One of the closest points on the curve x^(2) - y^(2) = 4 to the point (6,0) is

Find the point on the curve 3x^2-4y^2=72 which is nearest to the line 3x+2y+1=0.

One of the closed points on the curve x^(2) - y^(2)=4 to the point (6,0) is………

Find the points on the circle x^2+y^2-2x+4y-20=0 which are the farthest and nearest to the point (-5,6)dot

Find the points on the curve 5x^2-8x y+5y^2=4 whose distance from the origin is maximum or minimum.