(a)Define a parabola and derive its equation in the standard form `y^2=4ax`

Define ellipse and derive its equation in the form (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1(a gt b) .

If m and n are roots of a quadratic equation ,then the standard form of quadratic equations is:

What is adfected quadratic equations ? Write its standard form.

Define ideal gas. Derive ideal gas equation by using gas laws.

Find the slope of tangent to the curve if equation of the curve is y^2 = 4ax at (0,0)

Find the slope of normal to the curve if equation of the curve is y^2=4ax at (0 , 0)

The vertex of a parabola is (a,0) and the directrix is x+y=3a the equation of the parabola is