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  • Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise Fill in the blank question 10

Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise Fill in the blank question 10

Answers (1)

Answer:

 1

Hint:

 Use formulae of circumantce after finding c0-ordinates

Given:

x + αy  +2 = 5 

Solution:

Given equation of plane

x + \alpha y +2=5\Rightarrow \frac{x}{5}+\frac{\alpha y}{5}+\frac{z}{5}=1

Comparing above equation with equation of plane in intercept from

\frac{x}{x_{1}}+\frac{y}{y_{1}}+\frac{z}{z_{1}}=1

x_1=5,y_1=5,z_1=5

So coordinates of points A,B,C?A(5,0,0),B(0,5,0),C(0,0,5)

Let circumentre D(x,y,z)

\therefore AD=\sqrt{(x-5)^{2}+y^{2}+z^{2}}, BD=\sqrt{x^{2}+(y-5)^{2}+z^{2}}, CD=\sqrt{x^{2}+y^{2}+(z-5)^{2}}

AD=BD=CD ?  taking AD=BD

\Rightarrow \sqrt{(x-5)^{2}+y^{2}+z^{2}}=\sqrt{x^{2}+(y-5)^{2}+z^{2}}

On squaring both sides

(x - 5)2 + y2 + z2 = x2 + (y - 5)2 + z2 ? 1 = 1

∴  from equation (1) ,x,y  can be x=1, y=1

∴ α=1 (also)(by solving)

Posted by

Gurleen Kaur

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