The equations of the tangents to the circle $x^{2} + y^{2} = 13$ at the points whose abscissa is $2$ , are

2 x + 3 y = 13, 2 x - 3 y = 13

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3 x + 2 y = 13, 2 x - 3 y = 13

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2 x + 3 y = 13, 3 x - 2 y = 13

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None of the above

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Solution

The correct option is A $2 x + 3 y = 13, 2 x - 3 y = 13$
Let $(x_{1}, y_{1})$ be the co-ordinates of the point of contact,

The equation of tangent to the circle will be $x x_{1} + y y_{1} = 13$

Let the point be $(2, y_{1})$ , then

$2^{2} + y_{1}^{2} = 13$

$\Rightarrow y_{1} = \pm 3$

Hence, the required tangents are $2 x \pm 3 y = 13$

Suggest Corrections

Similar questions

x^{2} + y^{2} = 81,

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2 x - 3 y + 13 = 0

3 x - 2 y + 12 = 0

\frac{1}{2 x} + \frac{1}{3 y} = 2

\frac{1}{3 x} + \frac{1}{2 y} = \frac{13}{6}

x + y

2 x + 3 y = 12

3 x + 2 y = 13

Solve the pair of linear equations:

1/2x+1/3y=2

1/3x+1/2y=13/6

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