R K Bansal Solutions for Exercise 2: EXERCISE

Point $P(2,-7)$ is the centre of a circle with radius $13$ units, $PT$ is perpendicular to chord $\mathrm{AB}$ and $\mathrm{T}=(-2,-4)$
If the length of $\mathrm{AT}$ is $k$ units, find $k$.

Point is the centre of a circle with radius $13$ unit, $PT$ is perpendicular to chord $\mathrm{AB}$ and $\mathrm{T}=(-2,-4)$
If the length of the chord $\mathrm{AB}$ is $k$ units, find $k$.

Calculate the distance between the points $\mathrm{P}(2,2)$ and $Q(5,4)$ correct to three significant figures.

If the distance between $\mathrm{A}(7,3)$ and $\mathrm{B}$ on the $x$-axis whose abscissa is $11$ is $k$ units, find $k$.

If the distance between $\mathrm{A}(5,-3)$ and $B$ on the $y$-axis whose ordinate is $9$ is $k$ units, find $k$.

Find the point on $y$-axis whose distances from the points $A(6,7)$ and $B(4,-3)$ are in the ratio $1:2$.

The distances of point $\mathrm{P}(x,y)$ from the points $\mathrm{A}(1,-3)$ and $\mathrm{B}(-2,2)$ are in the ratio $2:3$. Show that $5x^2+5y^2-34x+70y+58=0$.

The points $\mathrm{A}(3,0), \mathrm{B}(a,-2)$ and $\mathrm{C}(4,-1)$ are the vertices of triangle $\mathrm{ABC}$ right-angled at vertex $A$. Find the value of $a$.