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  • If a circle, whose centre is touches the straight line <img alt="x+2 y+12=0," src="https://entrancecorner.onc

If a circle, whose centre is (-1,1) touches the straight line x+2 y+12=0, then the coordinates of the point of contact are

Option: 1

\left(-\frac{7}{2},-4\right)


Option: 2

\left(-\frac{18}{5},-\frac{21}{5}\right)


Option: 3

(2,-7)


Option: 4

(-2,-5)


Answers (1)

best_answer

Let point of contact be P\left(x_1, y_1\right) .

   This point lies on the given line ,  \therefore x_1+2 y_1=-12                   .....(i)

Gradient of O P=m_1=\frac{y_1-1}{x_1+1} ,    Gradient of x+2 y+12=m_2=-\frac{1}{2}

Both are perpendicular, \therefore \quad m_1 m_2=-1

\Rightarrow\left(\frac{y_1-1}{x_1+1}\right)\left(\frac{-1}{2}\right)=-1 \Rightarrow y_1-1=2 x_1+2 \Rightarrow 2 x_1-y_1=-3 \ldots \ldots \text { (ii) }

On solving the equation (i) and (ii), \left(x_1, y_1\right)=\left(\frac{-18}{5}, \frac{-21}{5}\right)

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Ritika Harsh

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