Prove that the curve represented by x=3(cost+sint),y=4(cost−sint),t∈R, is an ellipse
A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x–axis.
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
Two points O(0,0) and A(3,3) with another point P form an equilateral triangle. Find the coordinates of P˙
If two equal chords of a circle intersect within the circle, prove that the segments ofone chord are equal to corresponding segments of the other chord.
Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas:(i) 9x2−16y2=1 (ii) y2−16x2=1