Home
Class 12
MATHS
If x cos alpha +y sin alpha = 4 is tange...

If `x cos alpha +y sin alpha = 4` is tangent to `(x^(2))/(25) +(y^(2))/(9) =1`, then the value of `alpha` is

A

`tan^(-1)(3//sqrt(7))`

B

`tan^(-1)(7//3)`

C

`tan^(-1)(sqrt(3)//7)`

D

`tan^(-1)(3//7)`

Text Solution

Verified by Experts

The correct Answer is:
A
`x cos alpha + ysin alpha =4`
`:. y = (-cot alpha) x + 4 cosec alpha`
`:. m =- cot alpha, c = 4 cosec alpha, a^(2) = 25, b^(2) =9`
Now `c^(2) = a^(2)m^(2) + b^(2)`
`:. 16 cosec^(2) alpha = 25 cot^(2) alpha +9`
`:. 16 (1+cot^(2) alpha) = 25 cot^(2) alpha +9`
`:. 7 = 9 cot^(2) alpha rArr cot alpha = (sqrt(7))/(3) rArr tan alpha = (3)/(sqrt(7))`
`:. alpha = tan^(-1) (3//sqrt(7))`
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

  • ELLIPSE AND HYPERBOLA

    CENGAGE|Exercise Question Bank|1 Videos

Similar Questions

Explore conceptually related problems

If two distinct tangents can be drawn from the point (alpha, alpha+1) on different branches of the hyperbola (x^(2))/(9)-(y^(2))/(16)=1 , then find the values of alpha .

If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^2)+(y^2)/(b^2)=1 , then prove that a^2cos^2alpha+b^2sin^2alpha=p^2dot

If tangent of y^(2)=x at (alpha,beta) , where betagt0 is also a tangent of ellipse x +2y^(2)=1 then value of alpha is

If sin alpha + cos alpha = b, then sin 2 alpha is equal to

Let alpha , beta be such pi lt alpha- beta lt 3 pi if sin alpha + sin beta = (-21)/(65) , and cos alpha Cos beta = (-27)/(65) then the value of cos ( alpha - beta)/(2) is

if cos alpha + sin alpha = 3/4 , then sin ^6 alpha + cos ^6 alpha =

If x = cos alpha + i sin alpha , y = cos beta + i sin beta , prove that x^(m)y^(n)+1/(x^m y^n) = 2 cos (m alpha + n beta) .