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Syllabus

Let tangents drawn from point (0,5) to the ellipse = 1 are perpendicular and meet major axis of ellipse at points A & B. A hyperbola 'H' is drawn whose eccentricity is reciprocal of eccentricity of ellipse & whose foci are points A & B, then- (1) eccentricity of ellipse is (2) hyperbola 'H' is = 25 (3) hyperbola 'H' is 4x

^{2}– 12y^{2}= 75 (4) Length of latus rectum of ellipse isa) -85<m<-35 b) -35<m<15 c) 15<m<65 d) 35<m<85

a,b),two tangents PQ andPR are drawn to a circle x2+y2-a2=0.Find the equation of the circumcircle of triangle PQRA)2ROOT2 B)2 C)3-ROOT2 D)ROOT2

x

^{2}/b^{2}+ y^{2}/(b^{2}+a^{2}) =1^{2}+ y^{2}= 9 . The tangents at A and B intersect at C . If M (1,2) is the mid-point of AB than the area of triangle ABC is = ?^{2}=4px is of length 8p; prove that the lines from the vertex to its two ends are at right angles.Q26. If the lines a

_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2}=0 cut the coordinate axes in concyclic points, then(a) a

_{1}b_{1}= a_{2}b_{2}(b) $\frac{{\mathrm{a}}_{1}}{{\mathrm{a}}_{2}}=\frac{{\mathrm{b}}_{1}}{{\mathrm{b}}_{2}}$(c) a

_{1}+ a_{2}= b_{1}+ b_{2}(d) a_{1}a_{2}= b_{1}b_{2}ation of the locus of the mid- points of the chords of the circle x^{2}+ y^{2} = 9 which subtend an angle of 2 pi/3 at its centre is = ?Q. A circle is drawn such that it passes through the point 0, 1 and touches the parabola y = 2x

^{2}at (1, 2) tangents are drawn fromthe points p (8/3, 10/3) to touch the circle at a and b. The diameter of the circle circumscribing the triangle pab is ?

a) (-3/2 , 0) b) (-5/2 , 2) c) (-3/2 , 5/2 ) d) (-4 , 0 )