Let P be the point (1, 0) and Q a point on the locus y² = 8x. The locus of mid point of PQ is

• y² – 4x + 2 = 0

• y² + 4x + 2 = 0

• x² + 4y + 2 =

• x² + 4y + 2 =

• an ellipse

• a circle

• a straight line

• a straight line

223.

The locus of a point P (α, β) moving under the condition that the line y = αx + β is a tangent to the hyperbola 

• an ellipse

• a circle

• a parabola

• a parabola

If the circles x² + y² + 2ax + cy + a = 0 and x² + y² – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x + by – a = 0 passes through P and Q for

• exactly one value of a

• no value of a

• infinitely many values of a

• infinitely many values of a

A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is 

• an ellipse

• a circle

• a hyperbola

• a hyperbola

If a circle passes through the point (a, b) and cuts the circle x² + y² = p² orthogonally, then the equation of the locus of its centre is 

• x² + y² – 3ax – 4by + (a² + b² – p² ) = 0

• 2ax + 2by – (a² – b² + p² ) = 0

• x² + y² – 2ax – 3by + (a² – b² – p² ) = 0

• x² + y² – 2ax – 3by + (a² – b² – p² ) = 0

An ellipse has OB as semi-minor axis, F and F′ its focii and the angle FBF′ is a right angle. Then the eccentricity of the ellipse is

• 

• 1/2

• 1/4

• 1/4

If the pair of lines ax² + 2(a + b)xy + by² = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then

• 3a² – 10ab + 3b² = 0

• 3a² – 2ab + 3b² = 0

• 3a² + 10ab + 3b² = 0

• 3a² + 10ab + 3b² = 0

If |z²-1|=|z|²+1, then z lies on

• the real axis

• an ellipse

• a circle

• a circle

If a circle passes through the point (a, b) and cuts the circle x² +y²= 4 orthogonally, then the locus of its centre is

• 2ax +2by + (a² +b²+4)=0

• 2ax +2by - (a² +b²+4)=0

• 2ax -2by - (a² +b²+4)=0

• 2ax -2by - (a² +b²+4)=0