Recent questions and answers in Conic Sections

The equation of the ellipse whose focus is $(1,-1)$ ,the directrix the line $x-y-3=0$ and eccentricity $\large\frac{1}{2}$ is

answered Mar 6, 2019 by meiopde4

2 answers

Let $(x_1,y_1)$ be the point of intersection of the tangent to the parabola $y^2=4ax$ at the points $t_1$ and $t_2$ . Then $x_1=a{t_1}{t_2}$ and $y_1=a(t_1+t_2)$

answered Feb 20, 2015 by meena.p

1 answer

how to remember equation of tangent . can you show how did you find out Equation of tangent at $(a{t_1}^2,2a{t_1})$ is

answered Feb 20, 2015 by vijayalakshmi.r

1 answer

locus of the point of intersection of tangent to $y^2=4ax$ which intercept a constant length d on the directrix

answered Jan 19, 2015 by meena.p

1 answer

Show that the point $(x,y)$ given by $x=\large\frac{2at}{1+t^2}$ and $y=\large\frac{a(1-t^2)}{1+t^2}$ lies on a circle for all real values of $t$ such that $-1\leq t \leq 1$ where $a$ is any given real numbers.

answered Oct 17, 2014 by sreemathi.v

1 answer

Equation of the hyperbola with eccentricity $\large\frac{3}{2}$ and foci at $(\pm 2,0)$ is

answered Oct 17, 2014 by sreemathi.v

1 answer

The distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt 2$ .Its equation is

answered Oct 17, 2014 by sreemathi.v

1 answer

The eccentricity of the hyperbola whose latus rectum is $8$ and conjugate axis is equal to half of the distance between the foci is

answered Oct 17, 2014 by sreemathi.v

1 answer

If $e$ is the eccentricity of the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}\normalsize =1\;(a < b)$ ,then

answered Oct 17, 2014 by sreemathi.v

1 answer

The length of the latus rectum of the ellipse $3x^2+y^2=12$ is

answered Oct 16, 2014 by sreemathi.v

1 answer

If the vertex of the parabola is the point $(-3,0)$ and the directrix is the line $x+5=0$ ,then its equation is

answered Oct 16, 2014 by sreemathi.v

1 answer

If the parabola $y^2=4ax$ passes through the point $(3,2)$ ,then the length of its latus rectum is

answered Oct 16, 2014 by sreemathi.v

1 answer

If the focus of a parabola is $(0,-3)$ and its directrix is $y=3$ ,then its equation is

answered Oct 16, 2014 by sreemathi.v

1 answer

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length $3a$ is

answered Oct 16, 2014 by sreemathi.v

1 answer

Equation of the circle with centre on the $y$ -axis and passing through the origin and the point $(2,3)$ is

answered Oct 16, 2014 by sreemathi.v

1 answer

Equation of a circle which passes through $(3,6)$ and touches the axes is

answered Oct 16, 2014 by sreemathi.v

1 answer

The area of the circle centred at $(1,2)$ and passing through $(4,6)$ is

answered Oct 16, 2014 by sreemathi.v

1 answer

The equation of the hyperbola with vertices at $(0,\pm 6)$ and eccentricity $\large\frac{5}{3}$ is _ and its foci are ___

answered Oct 16, 2014 by sreemathi.v

1 answer

The equation of the parabola having focus at $(-1,-2)$ and the directrix $x-2y+3=0$ is _________

answered Oct 16, 2014 by sreemathi.v

1 answer

The equation of the ellipse having foci $(0,1),(0,-1)$ and minor axis of length $\sqrt 5$ is ____________

answered Oct 16, 2014 by sreemathi.v

1 answer