Many organic compounds contain more than one functional group. Which of the following is both an aldehyde and an ether
i) 
ii) 
iii) 
iv) 
v) 

The IUPAC name of the following compound is:

If the line x + y = k is a normal to the parabola y² = 4x,then the value of k will be-

the equation of tangent and normal in terms of the slope of the parabola are used to find the equations for any given slope.

The equation of the normal to the parabola x² = 8y whose slope is 1/m is

equations of normal and tangent in terms of the slope are used to find the normal and tangent for any given slope.

The equation of the normal to the parabola y² + 12x = 0 at the upper end of it's latus rectum is

the normal and tangent are always perpendicular to each other at any given point. Therefore, the product of slopes of tangent and normal is equal to -1.

The equation of the normal having slope m of the parabola y² = x + a is

parametric form of slope of parabola = y+tx = 2at + at^3

Find the equation of normal to the curve 2y = 3–x² at the point (1, 1)

equation of straight line :
(y-y1)=m(x-x1)

The equations of the normal at the ends of the latus rectum of the parabola y² = 4ax are given by-

the slope of normal = -1/ slope of tangent.
Equation of both normals can be generalized by multiplying both the equations.

The line x + my + n = 0 is a normal to the parabola y² = 4 ax if-

equation of normal of a parabola is given by:
y = -tx + 2at + at3

The equation of the normal to the parabola y² = 16 x with slope – 1/4 is-

equation of normal of a parabola is given by:
y = -tx + 2at + at3
equation of  normal in slope form: y = mx – 2am – am³

The equation of normal on point (2,4) to the parabola y² = 8x is-

we can also use equation of normal in slope form: y = mx – 2am – am³

Area of triangle formed by the tangents at three points t₁, t₂ and t3 of the parabola y² = 4ax is-

area under a triangle is given by the determinant of the vertex points of the triangle.

The equation of the common tangents to the parabolas y² = 4x and x² = 32y is-

the equation of tangent to the parabola y²= 4ax  is y = mx + a/m

The equation of tangent to the parabola x² = y at one extremity of latus rectum in the first quadrant is

equation of tangent : T=0 of
X²= 4ay is given by 
xx1=(y+y1)/2

The point of contact of the line 2x – y + 2 = 0 with the parabola y² = 16 x is-

for a line to be a tangent of a parabola, the value of a/m should be equal to the value of c.

The point on the curve y² = x the tangent at which makes an angle of 45º with x-axis will be given by

the point of contact of a tangent with the curve is given by (x,y) =(a/m², 2a/m). this is obtained by solving the equation of tangent with the equation of curve.