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Question

If the line 3x+4y=√7 touches the ellipse 3x2+4y2=1,
then the coordinates of the point of contact is .

A
(73, 0)
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B
(17,17)
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C
(0, 74)
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D
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Solution

The correct option is B (17,17)
Let the given line touches the ellipse
at (x1, y1),
then the equation of line is
3x1x+4y1y = 1
comparing it to given equation
3x+4y = 737x+47y = 1
We have 3x1 = 37x1 = 174y1 = 47y1 = 17
So, the point of contact is (17, 17)

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