A parabola has the origin as its focus and the line x=2as the directrix. Then the vertex of the parabola is at
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The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Find the equation for the ellipse that satisfies the given conditions:Foci (±3,0),a=4
Find the equation of a circle with centre (2, 2) and passes through the point (4, 5).
The line joining A(bcosαbsinα)
is produced to the point M(x,y)
so that AM
are in the ratio b:a˙
Then prove that x+ytan(α+2β)=0.
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.49x2+36y2=1
Find the equation of the circle with centre : (−2,3)and radius 4
Find the equations of the hyperbola satisfying the given conditions :Foci (±35,0), the latus rectum is of length 8.