Asked by 2 years ago
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 $x=a\cos\theta$...

1 answers and 29 views

Asked by 2 years ago
Find the equation of the bisectors of the angles between the lines $4x+3y-12=0$ and $y=3x$.

1 answers and 17 views

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

1 answers and 15 views

Asked by 2 years ago
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...

1 answers and 13 views

Asked by 2 years ago
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...

1 answers and 12 views

Asked by 2 years ago
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...

1 answers and 7 views

Asked by 2 years ago
Find the equation of the line joining the points $(a,0)$, $(0,b)$.

1 answers and 12 views

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

1 answers and 7 views

Asked by 2 years ago
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.

1 answers and 14 views

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

1 answers and 7 views

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

1 answers and 6 views

Asked by 2 years ago
Given $|z|=10$ and $arg z=120^o$, write down $z$

1 answers and 7 views

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

1 answers and 8 views

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

1 answers and 5 views

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

1 answers and 6 views

Asked by 2 years ago
Solve the following equation $2x^2-6x-3=0$

1 answers and 8 views

Asked by 2 years ago
Solve the following equation $5x^2-6x-2=0$

1 answers and 10 views

Asked by 2 years ago
Solve the equation $2x^2+7x-15=0$

1 answers and 6 views

Asked by 2 years ago
Find the remainder when $4x^3-6x+5$ is divided by $2x+1$.

1 answers and 4 views

Asked by 2 years ago
The roots of the equation $2x^2-7x+4=0$ are $\alpha$, $\beta$. Find an equation with integral coefficients whose roots are $\frac{\alpha}{\beta}$, $\frac{\beta}{\alpha}$.

1 answers and 17 views


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