Mathematics - Circle Question with Solution | TestHub

MathematicsCircleTangent & NormalMedium2 minQB

MathematicsMediuminteger

The tangents drawn from the origin to the circle $x^{2} + y^{2} - 2 r x - 2 h y + h^{2} = 0$ are perpendicular then sum of all possible values of $\frac{h}{r}$ is

Answer:

Solution:

Combined equation of the tangents drawn from $(0, 0)$ to the circle is $(x^{2} + y^{2} - 2 r x - 2 h y + h^{2}) h^{2} = (- r x - h y + h^{2})^{2}$ here coefficient of

$x^{2} + coffecient of y^{2} = 0 \Rightarrow (h^{2} - r^{2}) + (h^{2} - r^{2}) = 0 \Rightarrow \frac{h}{r} = \pm 1$

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Tangent & Normal

⏱ 2mℹ️ Source: QB

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