# Need solution for RD Sharma maths Class 12 Chapter 28 The Plane Exercise 28.9 Question 10 textbook solution.

Answer : The answer of the given question is  $37 x+20 y-21 z=61,67 x-20 y+99 z=121$

Hint :

$P=\left|\frac{a x_{1}+b y_{1}+c z_{1}+d}{\sqrt{a^{2}+b^{2}+c^{2}}}\right|$

Solution :  Let $(x,y)$ be a point which is equidistant from the given plane. Then,

\begin{aligned} &\frac{|3 x-4 y+12 z-6|}{\sqrt{9+16+144}}=\frac{|4 x+3 z-7|}{\sqrt{16+9}} \\ &\frac{3 x-4 y+12 z-6}{13}=\pm \frac{4 x+3 z-7}{5} \end{aligned}

\begin{aligned} &15 x-20 y+60 z-30=52 x+39 z-91 ; 15 x-20 y+60 z-30=-52 x-39 z+91 \\ &37 x+20 y-21 z=61 ; 67 x-20 y+99 z=121 \end{aligned}

Therefore this is the required equation

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