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Question

If the line 2x + 6y = 2 is tangent to the hyperbola x2 2y2 = 4 then the point of contact is.


A

(6,1)

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B

(2,6)

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C

(1,6)

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D

(4,6)

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Solution

The correct option is D

(4,6)


There is a set of questions in which we can compare 2 equations representing the same curve and find the parameters. This question is one among them.

We are asked the point of contact. We know the standard form of a tangent at a point (x1, y1). This equation can be compared with the given equation of tangent to

find out the point of contact.

The given hyperbola is,

x2 2y2 = 4

the tangent at a point (x1, y1) is,

xx1 2yy1 4 = 0

Now we compare it with the given tangent which is said to be the same after making the constant term the same by multiplying with a constant number if needed.

2x+6y2=0

i.e.,4x+26y4=0

x1=4

2y1=26

y1=6

(x1, y1)=(4,6)


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