Embibe Experts Solutions for Exercise 6: Assignment

The image of the centre of a circle $(x-2{)}^2+(y-1{)}^2=9$ w.r.t. the line $y=x$ moves $\sqrt{2}$ units along $(N-E)$ direction then the co-ordinates of the centre in the new position is

The equation of the circle whose radius is $5$ and which touches the circle $x^2+y^2-2x-4y-20=0$ externally at the point $\left(5, 5\right)$, is $x^2+y^2-18x+\lambda y+\mu =0$ then $\left(\lambda +\mu \right)$ is equal to

A circle has radius $3$ units and its centre lies on the line $y=x-1$. If the circle passes through point $\left(7, 3\right)$ and has centre at point $\left(h, k\right)$ then $h^k$ is

If the length of the tangent from any point on the circle $(x-3{)}^2+(y+2{)}^2=5r^2$ to the circle $(x-3{)}^2+(y+2{)}^2=r^2$ is $16$ units, then the area between the two circles is $\lambda \pi$ sq. units then $\lambda$ is equal to

The point of contact of the tangent to the circle $x^2+y^2=5$ at the point $\left(1, -2\right)$ which touches the circle $x^2+y^2-8x+6y+20=0$, is $\left(h, k\right)$ then $\left(2h^2+3k^2\right)$ is equal to

The equation of the circle having the lines $x^2+2xy+3x+6y=0$ as its normals and having size just sufficient to contain the circle $x\left(x-4\right)+y\left(y-3\right)=0$ is $x^2+y^2+\lambda x-3y-\mu =0$, where $\lambda , \mu \in N,$ then $\left(\lambda +\mu \right)$ is equal to

If the circles of same radius $a$ and centres at $\left(2, 3\right)$ and $\left(5, 6\right)$ cut orthogonally, then $a$ is equal to

The length of the diameter of the circle which cuts three circles $x^2+y^2-x-y-14=0,x^2+y^2+3x-5y-10=0,x^2+y^2-2x+3y-27=0$ orthogonally is