**difficulty:** medium **type:** mcq **focus:** tangent-normal-angle The tangent and normal at P on x^2/a^2 + y^2/b^2 = 1 meet the major axis at T and G. Then TG subtends a right angle at:

**difficulty:** hard **type:** mcq **focus:** ellipse-from-conditions An ellipse has foci at (+/-2, 0) and passes through (2, 3). Its equation is:

**difficulty:** hard **type:** mcq **focus:** locus-of-midpoint The locus of the midpoint of chords of x^2/9 + y^2/4 = 1 that subtend a right angle at the centre is:

**difficulty:** medium **type:** mcq **focus:** tangent-intercept-sum The sum of the squares of the reciprocals of two perpendicular diameters of x^2/a^2 + y^2/b^2 = 1 is:

**difficulty:** medium **type:** mcq **focus:** eccentricity-from-relation If the distance between the directrices of x^2/a^2 + y^2/b^2 = 1 is 3 times the distance between the foci, then e equals: