રેખાઓ 3 x-2 y=5 અને 3 x+2 y=5 થી સમાન અંતરે આ | vedclass

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

Question

Given lines are

${3x - 2y = 5}$......$(1)$

and    ${3x + 2y = 5}$.....$(2)$

Let $(h, k)$ is any point, whose distances from th

Vedclass · Accepted Answer

Vedclass · Answer

Given lines are

${3x - 2y = 5}$......$(1)$

and    ${3x + 2y = 5}$.....$(2)$

Let $(h, k)$ is any point, whose distances from the lines $(1) $ and $(2)$ are equal. Therefore

$\frac{{|3h - 2k - 5|}}{{\sqrt {9 + 4} }} = \frac{{|3h + 2k - 5|}}{{\sqrt {9 + 4} }}$

${	ext{or }}|3h - 2k - 5| = |3h + 2k - 5|$

${{	ext{which gives }}3h - 2k - 5 = 3h + 2k - 5{	ext{ or }} - (3h - 2k - 5)}$

${ = 3h + 2k - 5}$

Solving these two relations we get $k=0$ or $h=\frac{5}{3} .$ Thus, the point $(h, k)$ satisfies the equations $y=0$ or $x=\frac{5}{3},$ which represent straight lines. Hence, path of the point equidistant from the lines $(1)$ and $(2)$ is a straight line.

રેખાઓ $3 x-2 y=5$ અને $3 x+2 y=5$ થી સમાન અંતરે આવેલ તમામ બિંદુઓનો પથ એક રેખા છે તેમ બતાવો.

Similar Questions

$\Delta PQR$ નાં શિરોબિંદુઓ$ P (2, 1), Q (-2, 3)$ અને $R (4, 5)$ હોય, તો શિરોબિંદુ $R$ માંથી દોરેલ મધ્યગાનું સમીકરણ મેળવો.