Which of the following curves are symmetric about X-axis? Or Y-axis? Or origin? `x^2 + y^2 - 2xy +1 = 0`.

Is the parabola y^2=4x symmetrical about x-axis?

At what points on the following curve, is the tangent parallel to x-axis? y = x^2 on [-2,2]

Find the points on the following curve at which the tangents are parallel to x-axis. y = x^3 - 3x^2 - 9x+7 .

Apply Rolle's theorem to find oint (or points) on the following curves where the tangent is parallel to x -axis. y = 16 - x^2 , x in [-1,1]

At what points on the following curve, is the tangent parallel to x-axis? y = cos x - 1 on [0,2pi]

Apply Rolle's theorem to find point (or points) on the following curves where the tangent is parallel to x -axis. y = -1 + cos x in [0,2pi]

Find the equation of the parabola which is symmetric about y-axis and passes through the point (2,-3) .

Find the equation of the parabola, which has vertex (0, 0) and is symmetric about y-axis and passes through the point (2, - 3).

Show that the differential equation that represents the family of all parabolas having their axis of symmetry coincident with the axis of x is y y_2+y1 2=0.

Let f(x)=(ax^2+bx+c)/(x^2+1) such that y=-2 is an asymptote of the curve y=f(x) . The curve y=f(x) is symmetric about Y-axis and its maximum values is 4. Let h(x)=f(x)-g(x) ,where f(x)=sin^4 pi x and g(x)=log_(e)x . Let x_(0),x_(1),x_(2)...x_(n+1) be the roots of f(x)=g(x) in increasing order Then, the absolute area enclosed by y=f(x) and y=g(x) is given by