Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1.$

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If the point $(2,3),(1,1),and(x,3x)$ are collinear, then find the value of $x,$ using slope method.

If line $3x−ay−1=0$ is parallel to the line $(a+2)x−y+3=0$ then find the value of $a˙$

Find the equation of the circle with radius 5 whose centre lies on x–axis and passes through the point (2, 3).

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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 $4x_{2}+23 xy+2y_{2}=1$ . Through what angle should the axes be rotated so that the term $xy$ is removed from the transformed equation.

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