Class 12

Math

3D Geometry

Conic Sections

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

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Determine $x$ so that the line passing through $(3,4)and(x,5)$ makes an angle of $135_{0}$ with the positive direction of the x-axis.

Find the equation of the circle with centre : $(−2,3)$and radius 4

Find the equation of the circle with centre :(0, 2) and radius 2

A beam is supported at its ends by supports which are 12 metres apart. Since the load is connected at its centre, there is a deflection f 3 cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection 1 cm?

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.$36x_{2}+4y_{2}=144$

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.$16x_{2}−9y_{2}=576$

Let $A(6,4)andB(2,12)$ be two given point. Find the slope of a line perpendicular to $AB˙$