Class 11

Math

Co-ordinate Geometry

Conic Sections

An arch is in the form of a semi–ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

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Find the equation for the ellipse that satisfies the given conditions:b = 3, c = 4, centre at the origin; foci on a x axis.

Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse $9x_{2}+4y_{2}=36$.

Find the locus of the foot of perpendicular from the point (2, 1) on the variable line passing through the point (0, 0).

The equation of curve referred to the new axes, axes retaining their directions, and origin $(4,5)$ is $X_{2}+Y_{2}=36$ . Find the equation referred to the original axes.

$AB$ is a variable line sliding between the coordinate axes in such a way that $A$ lies on the x-axis and $B$ lies on the y-axis. If $P$ is a variable point on $AB$ such that $PA=b,Pb=a$ , and $AB=a+b,$ find the equation of the locus of $P˙$

Find the centre and radius of the circles$x_{2}+y_{2}−8x+10y−12=0$

Find the locus of a point, so that the join of $(−5,1)$ and $(3,2)$ subtends a right angle at the moving point.

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.$y_{2}=12x$ $x_{2}=−16y$$y_{2}=10x$