Question

Let a tangent to the curve $9 x^2+16 y^2=144$ intersect the coordinate axes at the points $A$ and $B$. Then, the minimum length of the line segment $AB$ is

Answer 1

The correct answer is 7.
Equation of tangent at point $P(4cosθ,3sinθ)$ is $4xcosθ​+3ysinθ​=1$
So, A is $(4secθ,0)$ and point B is $(0,3cosecθ)$
Length $AB=16sec2θ+9cosec2θ​ =25+16tan2θ+9cot2θ​≥7$