Find the angle between the asymptotes of the hyperbola 16x2−9y2=1 .
Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas:(i) 9x2−16y2=1 (ii) y2−16x2=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.4x2+9y2=36
In any triangle ABC, if the angle bisector of ∠Aand 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.