Line 3x - 4y = 5 is a tangent to hyperbola {x^2} - 4{y^2} = 5 . point of contact is

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10-2. Parabola, Ellipse, Hyperbola

easy

The line $3x - 4y = 5$ is a tangent to the hyperbola ${x^2} - 4{y^2} = 5$. The point of contact is

A

$(3, 1)$

B

$(2, 1/4)$

C

$(1, 3)$

D

None of these

Solution

(a) Suppose point of contact be $(h, k)$,

then tangent is $hx – 4ky – 5 = 0 \equiv 3x – 4y – 5 = 0$ or $h = 3,\,k = 1$

Hence the point of contact is $(3, 1).$

Standard 11

Mathematics

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