Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the equation of tangents to the curve $4x_{2}−9y_{2}=1$ which are parallel to $4y=5x+7.$

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If three points are $A(−2,1)B(2,3),andC(−2,−4)$ , then find the angle between $ABandBC˙$

Determine the ratio in which the line $3x+y−9=0$ divides the segment joining the points (1,3) and $(2,7)˙$

If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points $(a_{2}+1,a_{2}+1)$ and $(2a,−2a),$ then find the orthocentre.

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 the foot of perpendicular from the point (2, 1) on the variable line passing through the point (0, 0).

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 2).

$AB$ is a variable line sliding between the coordinate axes in such a way that $A$ lies on the x-axis and $B$ lies on the y-axis. If $P$ is a variable point on $AB$ such that $PA=b,Pb=a$ , and $AB=a+b,$ find the equation of the locus of $P˙$

Find the orthocentre of the triangle whose vertices are $(0,0),(3,0),$ and $(0,4)˙$