NIMCET Conic Section Previous Year Questions (PYQs)
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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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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: $\boxed{\sqrt3y=x+3}$
The angle of intersection of the cardioids $r = a(1 + \cos\theta)$ and $r = a(1 - \cos\theta)$ is
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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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