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` (c)`a=-2,b=2` (d) `a=-2,b=-2`

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=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 aa n dbdot

If the parabola y=(a-b)x^2+(b-c)x+(c-a) touches x- axis then the line ax+by+c=0 passes through a fixed point

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

The vertex of a parabola is the point (a , b) and the latus rectum is of length ldot If the axis of the parabola is parallel to the y-axis and the parabola is concave upward, then its equation is (a) (x+a)^2=l/2(2y-2b) (b) (x-a)^2=l/2(2y-2b) (c) (x+a)^2=l/4(2y-2b) (d) (x-a)^2=l/8(2y-2b)

If lim_(xrarr0)(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, then (a) a=-3 and b=9/2 (b) a=3 and b=9/2 (c) a=-3 and b=-9/2 (d) a=3 and b=-9/2

A point on the ellipse x^2+3y^2=37 where the normal is parallel to the line 6x-5y=2 is (5,-2) (b) (5, 2) (c) (-5,2) (d) (-5,-2)

Let the parabolas y=x(c-x)a n dy=x^2+a x+b touch each other at the point (1,0). Then (a) a+b+c=0 (b) a+b=2 (c) b-c=1 (d) a+c=-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

The locus of the midpoints of the chords of the circle x^2+y^2-a x-b y=0 which subtend a right angle at (a/2, b/2) is (a) a x+b y=0 (b) a x+b y=a^2=b^2 (c) x^2+y^2-a x-b y+(a^2+b^2)/8=0 (d) x^2+y^2-a x-b y-(a^2+b^2)/8=0