NIMCET 2027 Conic Section Previous Year Questions (PYQs)
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations
Study Stuff for MCA Examinations
Showing 2 questions
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
1
2
3
4
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
1
2
3
4
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°
NIMCET 2027
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
NIMCET 2027
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
