If the parabola `y=a x^2-6x+b` passes through `(0,2)` and has its tangent at `x=3/2` parallel to the x-axis, then (a) `a=2,b=-2` (b) `a=2,b=2` `a=-2,b=2` (d) `a=-2,b=-2`

If the curve y=a x^2-6x+b pass through (0,2) and has its tangent parallel to the x-axis at x=3/2, then find the values of a and bdot

If the curve y=a x^2-6x+b pass through (0,2) and has its tangent parallel to the x-axis at x=3/2, then find the values of aa n dbdot

If (a , b) is the midpoint of a chord passing through the vertex of the parabola y^2=4x , then (a) a=2b (b) a^2=2b (c) a^2=2b (d) 2a=b^2

If x=asectheta and y=btantheta , then b^2x^2-a^2y^2= (a) a b (b) a^2-b^2 (c) a^2+b^2 (d) a^2b^2

The tangent to y=a x^2+b x+7/2a t(1,2) is parallel to the normal at the point (-2,2) on the curve y=x^2+6x+10 , then a=-1 b. a=1 c. b=5/2 d. b=-5/2

If a!=0 and the line 2b x+3c y+4d=0 passes through the points of intersection of the parabolas y^2=4a x and x^2=4a y , then (a) d^2+(2b+3c)^2=0 (b) d^2+(3b+2c)^2=0 (c) d^2+(2b-3c)^2=0 (d)none of these

If a circle passes through the point (a, b) and cuts the circle x^2 + y^2 = 4 orthogonally, then the locus of its centre is (a) 2ax+2by-(a^(2)+b^(2)+4)=0 (b) 2ax+2by-(a^(2)-b^(2)+k^(2))=0 (c) x^(2)+y^(2)-3ax-4by+(a^(2)+b^(2)-k^(2))=0 (d) x^(2)+y^(2)-2ax-3by+(a^(2)-b^(2)-k^(2))=0

The hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (2, ) and has the eccentricity 2. Then the transverse axis of the hyperbola has the length 1 (b) 3 (c) 2 (d) 4

Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at the vertex of the parabola. Then the tangents drawn to the parabola at A .and B will intersect at (a) (-4a ,0) (b) (-2a ,0) (-3a ,0) (d) none of these

If x=acostheta and y=bsintheta , then b^2x^2+a^2y^2= (a) a^2b^2 (b) a b (c) a^4\ b^4 (d) a^2+b^2