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Phrases Conic Section PYQ

Phrases PYQ
Equation of the common tangent touching the circle $(x-3)^2+y^2=9$ and the parabola $y^2=4x$ above the $x$-axis is





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Phrases Previous Year PYQ Phrases NIMCET 2008 PYQ

Solution

Let tangent be $y=mx+c$, $m>0$. Tangency with $y^2=4x$ gives $c=\dfrac1m$. Tangency with the circle gives $|3m-c|=3\sqrt{m^2+1}$. Solving gives $m=\dfrac1{\sqrt3},\ c=\sqrt3$. Equation: $\sqrt3y=x+3$ Answer: $\boxed{\sqrt3y=x+3}$
Phrases PYQ
The angle of intersection of the cardioids $r = a(1 + \cos\theta)$ and $r = a(1 - \cos\theta)$ is





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Phrases Previous Year PYQ Phrases NIMCET 2010 PYQ

Solution

At intersection: a(1 + cosθ) = a(1 – cosθ) ⇒ cosθ = 0 ⇒ θ = π/2 or 3π/2 Slope formula for polar curves shows angle of intersection = 90°

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