Class 12

Math

3D Geometry

Conic Sections

Let $A=(3,4)$ and $B$ is a variable point on the lines $∣x∣$ =6. IF $AB≤4$ , then find the number of position of $B$ with integral coordinates.

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Find the area of the triangle formed by the lines joining the vertex of the parabola $x_{2}=12y$to the ends of its latus rectum.

Express the polar equation $r=2cosθ$ in rectangular coordinates.

Find the area of the pentagon whose vertices are $A(1,1),B(7,21),C(7,−3),D(12,2),$ and $E(0,−3)$

Find the equation of a circle with centre (2, 2) and passes through the point (4, 5).

Two points $O(0,0)$ and $A(3,3 )$ with another point $P$ form an equilateral triangle. Find the coordinates of $P˙$

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that $OQ=12cm$. Length PQ is :(A) 12 cm (B) 13 cm (C) 8.5 cm (D) $119 $cm.

Convert $r=cosecθe_{rcosθ}$ into its equivalent Cartesian equation.

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.