Let centre be C(h,k) CQ=CP=r ⇒CQ2=CP2 (h−0)2+(k±0)2=CM2+MP2 h2+(k±2 b)2=k2+4a2 h2+k2+4b2±4bk=k2+4a2 Then, the locus of centre C(h,k) x2+4b2±4by=4a2 Hence, the above locus of the centre of circle is a parabola.
A circle cuts a chord of length 4 a on the x -axis and passes through a point on the y -axis, distant 2 b from the origin. Then the locus of the centre of this circle, is:
Held on 11 Jan 2019 · Verified 6 Jul 2026.
a hyperbola
an ellipse
a straight line
a parabola
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
Let the image of parabola $x^{2}=4 y$, in the line $x-y=1$ be $(y+a)^{2}=b(x-c)$, $a, b, c \in \mathrm{~N}$. Then $a+b+c$ is equal to
The distance between the points (3, 4) and (6, 8) is:
If the chord joining the points $\mathrm{P}_{1}\left(x_{1}, y_{1}\right)$ and $\mathrm{P}_{2}\left(x_{2}, y_{2}\right)$ on the parabola $y^{2}=12 x$ subtends a right angle at the vertex of the parabola, then $x_{1} x_{2}-y_{1} y_{2}$ is equal to
The distance between the parallel lines 3x + 4y - 7 = 0 and 3x + 4y + 8 = 0 is:
Let a point $A$ lie between the parallel lines $L_{1}$ and $L_{2}$ such that its distances from $L_{1}$ and $L_{2}$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle $A B C$, where the points $B$ and C lie on the lines $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$, respectively, is :
Work through every JEE Main Coordinate Geometry PYQ, year by year.