Home
Class 12
MATHS
the value of lambda for which the line 2...

the value of `lambda` for which the line `2x-8/3lambday=-3` is a normal to the conic `x^2+y^2/4=1` is:

A

`(3)/(8)`

B

`(1)/(2)`

C

`-(sqrt(3))/(2)`

D

`(sqrt(3))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Equation of normal to ellipse `x^(2) + (y^(2))/(4) =1` is
`(x)/(cos theta) -(2y)/(sin theta) =1 -4` (i)
Comparing with `2x -(8)/(3) lambda y =- 3`
`cos theta =(1)/(2), lambda = (3)/(4 sin theta) = (sqrt(3))/(2)`
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

  • EQAUTION OF STRAIGHT LINE AND ITS APPLICATION

    CENGAGE PUBLICATION|Exercise DPP 3.2|13 Videos

Similar Questions

Explore conceptually related problems

Find the value of m, for which the line y=mx + 25sqrt3/3 is a normal to the conic x^2 /16 - y^2 / 9 =1 .

The line 2x+y+lamda=0 is a normal to the parabola y^(2)=8x, is lamda =

The line y=x+lambda is tangent to the ellips 2x^2+3y^2=1 Then lambda is

Value of lambda such that the line (x-1)/2=(y-1)/3=(z-1)/lambda is _|_ to normal to the plane vec r.(2 vec i+3 vec j+4 vec k)=0 is a. -(13)/4 b. -(17)/4 c. 4 d. none of these

The value of m for which the straight line 3x-2y+z+3 = 0=4x-3y+4z+1. is parallel to the plane 2x-y+mz-2 = 0 is

Find the value of lambda for which the lines 3x+4y=5,5x+4y=4 and lambda x+4y=6 meet at a point.

Find the value of a for which the lines 2x+y-1=0 , a x+3y-3=0 , 3x+2y-2=0 are concurrent.

Find the set of values of lambda , for which the point (sqrt(4-lambda^2),lambda) lies outside the triangle formed by the lines (y-3)^2=3x^2 and y+sqrt3=0

Find the value of lambda such that the line (x-2)/(6)=(y-1)/( lambda)=(z+5)/(-4) is prependicular to the plane 3x-y-2z=7

Find the real values of lambda for which the following system of linear equations has non -trivial solutions: x+y-3z=0,( 1+lambda)x+(2+lambda)y-8z=0 , x-(1+lambda)y+(2+lambda)z=0 .