class 11

Math

Co-ordinate Geometry

Conic Sections

A circle S passes through the point (0, 1) and is orthogonal to the circles $(x−1)_{2}+y_{2}=16$ and $x_{2}+y_{2}=1$. Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)

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Prove that the area of the triangle whose vertices are $(t,t−2),(t+2,t+2),$ and $(t+3,t)$ is independent of $t˙$

An equilateral triangle is inscribed in the parabola $y_{2}=4ax$ where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas:(i) $9x_{2} −16y_{2} =1$ (ii) $y_{2}−16x_{2}=1$

The points $(−a,−b),(a,b),(a_{2},ab)$ are (a) vertices of an equilateral triangle (b) vertices of a right angled triangle (c) vertices of an isosceles triangle (d) collinear

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is(A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm

In any triangle ABC, if the angle bisector of $∠A$and perpendicular bisector of BCintersect, prove that they intersect on the circumcircle of the triangle ABC

If $(x_{i},y_{i}),i=1,2,3,$ are the vertices of an equilateral triangle such that $(x_{1}+2)_{2}+(y_{1}−3)_{2}=(x_{2}+2)_{2}+(y_{2}−3)_{2}=(x_{3}+2)_{2}+(y_{3}−3)_{2},$ then find the value of $y_{1}+y_{2}+y_{3}x_{1}+x_{2}+x_{3} $ .