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Question

If the line 3x + 4y = 12 is a tangent to the ellipse x216+y29=2 then find the point of contact.


A

(3, 4)

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B

(6, 8)

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C

(8, 6)

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D

(4, 8)

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Solution

The correct option is C

(8, 6)


We will assume the point to be P(x1, y1). We know how to find the tangent at (x1, y1) to the ellipse x216+y29=2

It is xx116+yy19=2 (T=0)

We will make the R.H.S equal to 12 So that we can compare it with the given equation of tangent

6× xx116+6×yy19=6× 2=12...(1)

3x + 4y = 12...(2)

is the equation given

(1)and (2) both represent the same equation

Comparing both the equations, we get

6x116=3 and 6y19=4

x1 = 8 and y1 = 6

(8,6) is the point at which the tangent is drawn.


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