If the lines 3x + 4y - 14 = 0 and 6x + 8y + 7 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given,the lines $3x + 4y - 14 = 0$ and $6x + 8y + 7 = 0$ are both tangents to a circle. We observe that both lines are parallel. Dividing the seco

Vedclass · Accepted Answer

$\frac{7}{4}$

Vedclass · Answer

(C) Given,the lines $3x + 4y - 14 = 0$ and $6x + 8y + 7 = 0$ are both tangents to a circle. We observe that both lines are parallel. Dividing the second equation by $2$,we get $3x + 4y + \frac{7}{2} = 0$. The distance between two parallel lines $ax + by + c_1 = 0$ and $ax + by + c_2 = 0$ is given by $d = \frac{|c_1 - c_2|}{\sqrt{a^2 + b^2}}$. The diameter of the circle is equal to the distance between these two parallel tangents. Diameter $= \frac{|-14 - \frac{7}{2}|}{\sqrt{3^2 + 4^2}} = \frac{|-\frac{28}{2} - \frac{7}{2}|}{\sqrt{9 + 16}} = \frac{|-\frac{35}{2}|}{5} = \frac{35}{10} = \frac{7}{2}$. Therefore,the radius of the circle is $r = \frac{	ext{Diameter}}{2} = \frac{7/2}{2} = \frac{7}{4}$.

If the lines $3x + 4y - 14 = 0$ and $6x + 8y + 7 = 0$ are both tangents to a circle,then its radius is

Similar Questions

Silica is added to roasted copper ore during extraction in order to remove

In which of the following is a closed circulatory system found?

An optical fibre communication system works on a wavelength of $1.3 \mu m$. The number of subscribers it can feed if a channel requires $20 \text{ kHz}$ is:

The maximum possible number of real roots of the equation $x^5 - 6x^2 - 4x + 5 = 0$ is

The tension $T$ in the string shown in the figure is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module