Maths-
General
Easy
Question
The number of real tangents that can be drawn to the ellipse 3x2 + 5y2 = 32 and 25x2 + 9y2 = 450 passing through (3 , 5) is
- 0
- 2
- 3
- 4
Hint:
find the position of the point with respect to the ellipse.
The correct answer is: 3
3
on substituting the point 3,5 on the equations of ellipses, we get
E1 : 3(9) + 5(25) – 32 = 120 , which is >0
E2 : 25(9) + 9(25) – 450 =0
Hence, 2 tangents can be drawn from the point on the first ellipse and 1 tangent can be drawn to the 2nd ellipse
Total = 2+1 = 3
if a point lies inside, no real tangents can be drawn from the point on the curve. on the curve, then only 1 tangent and if outside, then 2 tangents can be drawn.
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