Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse a2x2+b2y2=1.
Find the equation of the circle with radius 5 whose centre lies on x–axis and passes through the point (2, 3).
Fill in the blanks:(i) The centre of a circle lies in of the circle. (exterior/ interior)(ii) A point, whose distance from the centre of a circle is greater than its radius lies inof the circle. (exterior/ interior)(iii) The longest chord of a circle is a_________ of the circle.(iv) An arc is a _________when its ends are the ends of a diameter.(v) Segment of a circle is the region between an arc and________ of the circle.(vi) A circle divides the plane, on which it lies, in________ parts.
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.4x2+9y2=36
Two points P(a,0) and Q(-a,0) are given. R is a variable point on one side of the line PQ such that ∠RPQ−∠RQP is a positive constant 2α˙ Find the locus of the point R˙
Given the equation 4x2+23xy+2y2=1 . Through what angle should the axes be rotated so that the term xy is removed from the transformed equation.