The sum and product of the slopes of the tangents to the hyperbola `(x^2)/4-(y^2)/2=1` drawn from the point `(3,-2)` are (A) `-12/5,6/5` (B) `12/5,6/5` (C) `11/4,7/5` (D) `-12/5,8/5`

The angle between the tangents drawn at the points (5,12) and (12,-5) to the circle x^(2)+y^(2)=169is

The angle between the tangents drawn at the points (5,12) and (12,-5) to the circle x^(2)+y^(2)=169is

If the tangent drawn to parabola y=x^2-5x+5 at a point is parallel to 2y=4x+lamda . Then the tangent passes through the point. (A) (3/4, 5/2) (B) (-1/8, 7) (C) (1,3) (D) (1/8,-7)

Let A(4,-2) and B(0,1) are two points on the parabola,normals at which intersect at the point P(2,2). The equation of directrix of the parabola is (A)((6)/(5),-(6)/(5))(B)((16)/(5),-(7)/(5)) (C) ((12)/(5),-(6)/(5))(D)(-(6)/(5),(6)/(5))

Show that the point (1,2,3) is common to the lines which join A (4,8,12) to B (2,4,6), and c(3,5,4) to D(5,8,5).

If the eccentricity of the hyperbola (x ^(2))/(a ^(2)) -(y ^(2))/(b ^(2)) =1 is (5)/(4) and 2x + 3y - 6 =0 is a focal chord of the hyperbola, then the length of transvers axis is equal to a) 12//5 b) 6 c) 24//7 d) 24//5

Show that the point (1,2,3) is common to the lines which join A(4,8,12) to B(2,4,6) and C(3,5,4) to D(5,8,5)

The mean of 5 observations is 5 and their variance is 124. If three of the observationsare 1,2 and 6, then the mean deviation from the mean of the data is (1)2.4 (b) 2.8 (c) 2.5 (d) 2.6

If the tangent drawn to parabola y=x^(2)-5x+5 at a point is parallel to 2y=4x+lambda. Then the tangent passes through the point.(A) ((3)/(4),(5)/(2))(B)(-(1)/(8),7)(C)(1,3)(D)((1)/(8),-7)