Find the equation of the chord of the hyperbola 25x2−16y2=400 which is bisected at the point (5, 3).
Find the coordinates of the point which divides the line segments joining the points (6,3) and (−4,5) in the ratio 3:2 (i) internally and (ii) externally.
Find the equation for the ellipse that satisfies the given conditions:Major axis on the x–axis and passes through the points (4, 3) and (6, 2).
XYand XprimeYprimeare two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XYat A and XprimeYprimeat B. Prove that ∠AOB = 90o
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.16x2+9y2=1
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.
Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.