The number of possible tangents which can be drawn to the curve `4x^2-9y^2=36 ,` which are perpendicular to the straight line `5x+2y-10=0` , is zero (b) 1 (c) 2 (d) 4

Options

A. a. zero
B. b. 1
C. c. 2
D. d. 4

Answer

A

Explanation

Tangent to
`(x^(2))/(9)-(y^(2))/(4)=1`
at `P(3 sec theta, 2 tan theta)` is
`(x)/(3)sec theta-(y)/(2)tan theta=1`
This is perpendicular to ltBrgt `5x+2y-10=0`
`therefore" "(2 sec theta)/(3 tan theta)=(2)/(5)`
`"or "sin theta=(5)/(3)`
which is not possible.
Hence, there is no such tangent.