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MathematicsCircleEquation of chord with given middle point Chord of contact Pair of TangentsMedium2 minPYQ_2010

MathematicsMediumsingle choice

The line $a x + b y = 1$ cuts ellipse $c x^{2} + d y^{2} = 1$ only once if

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Solution:

Clearly $a x + b y = 1$ i.e $y = - \frac{a}{b} x + \frac{1}{b}$ is tangent to $cx^{2} + dy^{2} = 1 \Rightarrow \frac{x ^{2}}{\frac{1}{c}} + \frac{y ^{2}}{\frac{1}{d}} = 1 ∴ (\frac{1}{b})^{2} = (\frac{1}{c}) (- \frac{a}{b})^{2} + (\frac{1}{d}) \Rightarrow 1 = \frac{a ^{2}}{c} + \frac{b ^{2}}{d}$

Stream:BITSATSubject:MathematicsTopic:CircleSubtopic:Equation of chord with given middle point Chord of contact Pair of Tangents

⏱ 2mℹ️ Source: PYQ_2010

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