Let P be a point in the first quadrant lying on the ellipse `9x^2 + 16y^2 = 144`, such that the tangent at P to the ellipse is inclined at an angle of `135^@` to the positive direction of x-axis. The n the coordinates of P are

Options

A. `((16)/(5),(9)/(5))`
B. `((sqrt(143))/(3),(1)/(4) )`
C. `((8)/(9),(sqrt(77))/(3))`
D. `((4)/(sqrt(2)),(3)/(sqrt(2)))`

Answer

A

Explanation

m= slope of the tangent at P= `tan 135^(@)=-1.`
here ,`a^(2) = 16 and b^(2)=9 ` so the coordinates of the point of contact P are `(-(a^(2)m)/(sqrt(a^(2)m^(2)+b^(2))),(b^(2))/(sqrt(a^(2)m^(2)+b^(2))))=((16)/(5),(9)/(5))` as it lies in the quadrant .