Question

The total number of real tangents that can be drawn to the ellipse $3x^2+5y^2=32$ and $25x^2+9y^2=450$ passing through $(3,5)$ is

• A. $0$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

$(3,5)$ lies on $25x^2+9y^2=450$

Therefore, one tangent can be drawn

and $(3,5)$ lies outside $3x^2+5y^2=32$ because $S_1>0$

Therefore, two tangents can be drawn.

So total 3 tangents