Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the angle between the asymptotes of the hyperbola $16x_{2} −9y_{2} =1$ .

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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) $y_{2}−16x_{2}=1$

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.$4x_{2}+9y_{2}=36$

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

Find the equations of the hyperbola satisfying the given conditions :Foci $(0,±10 )$, passing through (2,3)

If the middle points of the sides of a triangle are $(−2,3),(4,−3),and(4,5)$ , then find the centroid of the triangle.

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 equation of the circle with centre : (1, 1) and radius $2 $

Find the area of a triangle having vertices $A(3,2),B(11,8),$ and $C(8,12)˙$