Question

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

• A. 0
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

Given : Equations of ellipses
$3x^2+5y^2=32$..(1)
& $25x^2+9y^2=450$...(2)
Tangents to the ellipse (1) & (2) are passing through the point (3, 5)
$\therefore 3(3{)}^2+5(5{)}^2-32=27+75-32>0$
So the given point lies outsides the ellipse. Hence, two real tangents can be drawn from the point to the ellipse
& $25(3{)}^2+9(5{)}^2-450=225+225-450=0$
$\therefore$ The point lie on the ellipse. Hence one
real tangent can be drawn.
$\therefore$ No. of real tangents = 3