Find the coordinates of the points where the line $4x-5y+6a=0$ cuts the curve given parametrically by $(at^2, 2at)$.

Obtain parametric equations for the locus $y^2=x^3-x^2$.

Consider a circle, radius $a$, center at the origin. Let $P(x, y)$ be any point on the circle, and let the angle between $PO$ and the x-axis be $\theta$, then $x=a\cos\theta$...

Find the equation of the bisectors of the angles between the lines $4x+3y-12=0$ and $y=3x$.

Find the distance of the points (a) $(1,3)$, (b) $(-3,4)$, (c) $(4,-2)$ from the line $2x+3y-6=0$.

Let $P$ be any point and let $OP=r$, where $O$ is the origin and let $OP$ make an angle $\theta$ with the axis, then $r$ and $\theta$ are called Polar coordinates of the point...

Let $P$ be any point and let $OP=r$, where $O$ is the origin and let $OP$ make an angle $\theta$ with the axis, then $r$ and $\theta$ are called Polar coordinates of the point...

Let $P$ be any point and let $OP=r$, where $O$ is the origin and let $OP$ make an angle $\theta$ with the axis, then $r$ and $\theta$ are called Polar coordinates of the point...

Find the equation of the line joining the points $(a,0)$, $(0,b)$.

Find the equation of the line with gradient $-\frac{2}{3}$, which passes through the point $(1,-4)$.

Find the coordinates of the points on the curve $y-x^2$, given by $x=4$ and $-10$, and find the gradient of the curve at these points.

Find the equation of the normal to the curve $y=(x^2+x+1)(x-3)$ at the point where it cuts the $x-axis$

Find the equation of the tangents to the curve $y=x^3$ at points $(2,8)$.

Given $|z|=10$ and $arg z=120^o$, write down $z$

Solve $x^2-6x+13=0$, where $x\epsilon \mathbb{c}$

Find, by completing the square, the greatest value of the function $f(x)=1-6x-x^2$

Express the function $f(x)=2x^2-12x+23$ in the form $a(x-p)^2+q$.

Solve the following equation $2x^2-6x-3=0$

Solve the following equation $5x^2-6x-2=0$
Solve the equation $2x^2+7x-15=0$