Vinod Singh and Shweta Pawar Solutions for Chapter: Circle and Conics, Exercise 3: Competitive Thinking

The centres of those circles which touch the circle $x^2+y^2-8x-8y-4=0$ externally and also touch the $X$-axis, lie on

Let $A$ be the centre of the circle $x^2+y^2-2x-4y-20=0$. Let $B\left(1,7\right)$ and $D\left(4,-2\right)$ be two points on the circle such that tangents at $B$ and $D$ meet at $C$. The area of the quadrilateral $ABCD$ is

Let the orthocentre and centroid of a triangle be $A(-3,5)$ and $B(3,3)$. respectively. If $C$ is the circumcentre of this triangle, then the radius of the circle having line segment $AC$ as diameter, is

The equation of a parabola, which passes through the point of intersection of a straight line $x+y=0$ and the circle $x^2+y^2+4y=0$, is

The lines $y=2x+\sqrt{76}$ and $2y+x=8$ touch the ellipse $\frac{x^2}{16}+\frac{y^2}{12}=1$. If the point of intersection of these two lines lie on a circle, whose centre coincides with the centre of that ellipse, then the equation of that circle is

If a bar of given length moves with its extremities on two fixed straight lines at right angles, then the locus of any point on bar marked on the bar describes a/an

The distance of midpoint of the line joining two points $(4,0)$ and $(0,4)$ from the centre of the circle $x^2+y^2=16$ is

Tangents are drawn to the hyperbola $4x^2-y^2=36$ at the points $P$ and $Q$. If these tangents intersect at the point $T\left(0, 3\right)$, then the area (in sq. units) of $△PTQ$ is