Name: Introduction to Straight lines
Uploaded: 2019-07-19
Duration: 25 min 10 s
Description: In this video, basic concepts of Straight lines are discussed. The content in this video is helpful to solve the related problems on this topic.

Question

The line joining the points $A (0, 5)$ and $B (4, 1)$ is a tangent to a circle whose centre $C$ is at the point $(4, 4)$ .

Find the equation of the line through $C$ which is perpendicular to the line $AB$ .

Accepted Answer

Equation of line $AB, A (0, 5)$ and $B (4, 1)$

$\frac{y - y_{1}}{y_{2} - y_{1}} = \frac{x - x_{1}}{x_{2} - x_{1}}$

$\Rightarrow \frac{y - 5}{1 - 5} = \frac{x - 0}{4 - 0}$

$\Rightarrow 4 (y - 5) = - 4 x$ gives $y - 5 = - x$ .

Hence, the required equation of the line $A B$ is $x + y - 5 = 0$ .

The equation of a line which is perpendicular to the line $AB$ : $x + y - 5 = 0$ is $x - y + k = 0$

Since it is passing through the point $(4, 4)$ , we have

$4 - 4 + k = 0$ gives $k = 0$

The equation of a line which is perpendicular to $AB$ and through $C$ is $x - y = 0$

The line joining the points $A (0, 5)$ and $B (4, 1)$ is a tangent to a circle whose centre $C$ is at the point $(4, 4)$ .

Find the equation of the line through $C$ which is perpendicular to the line $AB$ .

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

The line joining the points A(0,5) and B(4,1) is a tangent to a circle whose centre C is at the point (4,4). Find the equation of the line through C which is perpendicular to the line AB.

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

The line joining the points $A (0, 5)$ and $B (4, 1)$ is a tangent to a circle whose centre $C$ is at the point $(4, 4)$ .

Find the equation of the line through $C$ which is perpendicular to the line $AB$ .