##### In the previous article , we have solved few questions of Plane Chapter (Ex-2B) of S N De Mathematics(Chhaya). In the following article, we are going to discuss/solve Short Answer Type Questions of S.N.Dey Mathematics-Class 12 of the chapter Tangent and Normal (Ex-14).

1. If be a tangent to the circle at any given point then find the equation of the normal to the circle at the same point.

Solution.

Since the normal to the given circle is perpendicular to the straight line so the equation of the normal can be written as

Since the normal (1) passes through the center of the circle i.e., , we get from (1),

The equation of the normal to the circle is

2. If be a tangent to the circle at a given point on it, find the equation of the normal to the circle at the same point.

Solution.

By question, the equation of the normal can be written as

Since the normal passes through the center of the circle i.e., ,

Hence, the equation of the normal is given by

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3.(i) Find the points on the ellipse at which the tangents are parallel to x-axis. Also find the points on it where the tangents are parallel to y-axis.

Solution.

Let the tangents of (1) are parallel to x-axis at

Now, from (1) we get,

So, by (2) we get,

Since the point lies on ,

For we get from (4),

Hence, the required points are and

2nd Part :

Let the tangents drawn at on the given ellipse are parallel to y-axis.

So, in this case, the slope

lies on the given ellipse ,

Hence, the required points are

(ii) Is there any tangent parallel to x-axis to the parabola Give reasons for your answer.

Solution.

If possible, let the tangent to the parabola (1) is parallel to axis at the point

The slope of the tangent at is given by

In this case,

From (1) and (2) we get, which is impossible.

Hence, there is no tangent parallel to axis to the parabola

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(iii) Find where the normal to is parallel to x-axis.

Solution.

Differentiating both sides of (1) w.r.t. we get,

Suppose that the normal to the circle (1) is parallel to x-axis at

So, in this case, the slope of the normal

Since lies on (1),

Hence, the required points are and

4.(i) Find where the tangent to the parabola is parallel to the line

Solution.

Let the tangent to the parabola (1) at the point is parallel to the line (2).

In this case, slope of the tangent at the gradient of the straight line (2).

lies on the parabola (1),

Hence, the coordinates of the required point is

(ii) Find the coordinates of points on the hyperbola at which the normal is perpendicular to the line

Solution.

Suppose that normal to the hyperbola (1) at is perpendicular to the straight line (2).

Slope of normal to hyperbola (1) at Slope of the straight line (2)

Hence, from (3) and (4) we get,

Since the point lies on the hyperbola

For

For

Hence, the coordinates of the required points are

(iii) Prove that the tangent to the curve at the points and are at right angles. [CBSE ’92]

Solution.

Differentiating both sides of (1) w.r.t. we get

Slope of (1) at is given by

Again, slope of (1) at is given by

the result follows.

## Tangent and Normal | Part-2

In this article , we have solved few VSA type Questions (5-15) of S N De Mathematics, Tangent and Normal Chapter (Ex-14 ).

## S.N. De -Tangent and Normal (Part -1)-Class 12

In this book, full solutions of **S.N. De -Tangent and Normal (Part -1) (Eng. Version)-Class 12** have been provided. This book contains solutions of (Ex-14) and have solutions of Very Short Answer Type Questions and Short Answer Type Questions. This book contains 82 pages along with a cover page .

## Tangent and Normal | Part-3

In this article, we have solved VSA type questions from 16-26 of S N De Mathematics, Tangent and Normal Chapter (Ex-14 ).

## Tangent and Normal | Part-4

In this article , we have solved VSA type questions from 27-31 of S N De Mathematics, Tangent and Normal Chapter (Ex-14 ).

## Tangent and Normal | Part-5

In this article, we have solved Short Answer Type questions from 1-6 of S N De Mathematics, Tangent and Normal Chapter (Ex-14 ).

## Tangent and Normal | Part-6

In this article , we have solved Short Answer type questions from 7-13 of S N De Mathematics, Tangent and Normal Chapter (Ex-14 ).

## Tangent and Normal | Part-7

In this article , we have solved Short Answer Type questions from 14-26 of S N De Mathematics, Tangent and Normal Chapter (Ex-14 ).

## Tangent and Normal | Part-8

In this article , we have solved Short Answer type questions from 27-33 of S N De Mathematics, Tangent and Normal Chapter (Ex-14 ).

## Tangent and Normal | Part-9

In this article , we have solved Short Answer type questions from 34-40 of S N De Mathematics, Tangent and Normal Chapter (Ex-14 ).