# Equation of Normal at a Point (x,y) in Terms of f'(x)

## Trending Questions

**Q.**Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its center at (3, −4), one focus at (4, −4) and one vertex at (5, −4). If mx−y=4, m>0 is a tangent to the ellipse E, then the value of 5m2 is equal to

**Q.**

Let the line $y=mx$ and the ellipse $2{x}^{2}+{y}^{2}=1$ intersect a point P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at $\left(-\frac{1}{3\sqrt{2}},0\right)$ and $\left(0,\mathrm{\xce\xb2}\right)$, then $\mathrm{\xce\xb2}$ is equal to

$\frac{2}{\sqrt{3}}$

$\frac{2}{3}$

$\frac{2\sqrt{2}}{3}$

$\frac{\sqrt{2}}{3}$

**Q.**Let P(x0, y0) be a point on the curve C:(x2−11)(y+1)+4=0, where x0, y0∈N. If area of the triangle formed by the normal drawn to the curve C at P and the co-ordinate axes is ab, where a, b∈N, then the least value of a−6b is

**Q.**Let the normal at a point P on the curve y2−3x2+y+10=0 intersects the y-axis at (0, 32). If m is the slope of the tangent at P to the curve, them |m| is equal to

**Q.**The equation of the normal to the curve y=2x2+3 sin x at x = 0 is

- x + 3y = 0
- x - 3y = 0
- 3x - y = 0
- 3x + y = 0

**Q.**If the normal of y=f(x) at (0, 0) is given by y−x=0, then

limx→0x2f(x2)−20f(9x2)+2f(99x2)

- equals 12
- equals 119
- equals −119
- does not exist

**Q.**

What is the parametric form of the equation of the ellipse given by,

x^{2}/a^{2} + y^{2}/b^{2} = 1

**Q.**

For the straight lines 4x + 3y – 6 = 0 and 5x + 12y + 9 = 0, the equation of the bisector of the angle which contains the origin is

7x + 9y + 3 = 0

7x – 9y + 3 = 0

7x + 9y – 3 = 0

None of these

**Q.**

e^(sin x) - e^(-sin x) = 4 then find the number of real solutions

**Q.**The distance, from the origin, of the normal to the curve, x=2cost+2tsint, y=2sint–2tcost, at t=π4, is:

- 4
- √2
- 2
- 2√2

**Q.**Let S be the area bounded by the curve y=sinx, 0≤x≤π and the x−axis and T be the area bounded by the curves y=sinx, 0≤x≤π2, y=acosx, 0≤x≤π2 and the x−axis, where a∈R+. If S:T=1∶13, then which of the following is(are) CORRECT ?

- The value of a is 43
- The value of S is equal to 1.
- The value of T is equal to 23
- The value of a is 23

**Q.**Let C be a curve given by y(x)=1+√4x–3, x>34. If P is a point on C, such that the tangent at P has slope 23, then a point through which the normal at P passes, is:

- (3, −4)
- (1, 7)
- (2, 3)
- (4, −3)

**Q.**The abscissa of a point on the curve xy=(a+x)2, at which the normal cuts off numerically equal intercepts from the coordinate axes is

- −a√2

- √2 a

- a√2

- −√2 a

**Q.**The area of the region bounded by the curves |x+y|≤2, |x−y|≤2 and 2x2+6y2≥3 is

- (8+√32π)sq. units

- (8−√32π)sq. units

- (4−3√32π)sq. units

- (8−3√32π)sq. units

**Q.**The abscissa of the point on the curve √xy=a+x, the tangent at which cuts off equal intercepts from the coordinate axes is

- a√2
- −a√2
- −a√2
- a√2

**Q.**Let the line y=mx and the ellipse 2x2+y2=1 intersect at point P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at (−13√2, 0) and (0, β), then β is equal to:

- 23
- 2√23
- √23
- 2√3

**Q.**Let C(m, n) be a point on the curve y=x3, where the tangent is parallel to the chord connecting the points O(0, 0) and A(2, 8). Then the value of m⋅n is:

- 169
- 125
- 1627
- 329

**Q.**Which of the following statements is (are) INCORRECT about f(x)=exx?

- f(x) is increasing in (0, ∞).
- Tangent on the curve y=f(x) at x=1 is perpendicular to x−axis.
- Tangent on the curve y=f(x) at x=1 is parallel to x−axis.
- Range of f(x) is [e, ∞).

**Q.**36. dy/dx+2xtan(x-y)=1 then sin(x-y) (1) origin (2) the line x=1/2 (3)The point (1, 0) (4) the point (1/2, 0)

**Q.**The triangle formed by the normal to the curve f(x)=x2−ax+2a at the point (2, 4) and the coordinate axes lie in second quadrant. If its area is 2 sq.units, then the sum of possible values of a is

**Q.**The equation of the normal to the curve y=2x2+3 sin x at x = 0 is

- x + 3y = 0
- x - 3y = 0
- 3x - y = 0
- 3x + y = 0

**Q.**The area enclosed by the curve y=sinx+cosx and y=|cosx−sinx| over the interval [0, π2] is

- 4(√2−1)
- 2√2(√2−1)
- 2(√2+1)
- 2√2(√2+1)

**Q.**For the curve x=t2−1, y=t2−t, tangent is parallel to x - axis where,

- t=0
- t=12
- t=−1√3
- t=1√3

**Q.**The equation of the plane through the intersection of the planes x + 2y + 3z = 4 and 2x + y − z = −5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 is

(a) 7x − 2y + 3z + 81 = 0

(b) 23x + 14y − 9z + 48 = 0

(c) 51x − 15y − 50z + 173 = 0

(d) None of these

**Q.**Find the equation of the normals to the curve y = x 3 + 2 x + 6 which are parallel to the line x + 14 y + 4 = 0.

**Q.**The centre of a circle of radius 4√5 lies on the line y=x and satisfies the inequality 3x+6y>10. If the line x+2y=3 is a tangent to the circle, then the equation of the circle is

**Q.**Let [k] denote the greatest integer less than or equal to k. If S is the area enclosed by the curves f(x)=4|x|−|x|3 and g(x)+√4−x2=0, then the value of [S] is

**Q.**If the line aX + bY + c =0 is a normal to the curve xy =1. Then

- a > 0, b > 0
- a > 0, b=0
- a < 0, b > 0
- a < 0, b < 0

**Q.**If normal to the curve y = f(x) is parallel to x-axis, then correct statement is [RPET 2000]

- dydx=0
- dydx=1
- dxdy=0
- None of these

**Q.**If A is (x1, y1) where x1=1 on the curve y=x2+x+10, the tangent at A cuts the x-axis at B. The value of ¯¯¯¯¯¯¯¯OA.¯¯¯¯¯¯¯¯AB is

- 148
- −352
- −148
- 140