18. Find the coordinates of a point on y-axis which are at a distance of   from the point P (3, –2, 5).

18. Let Q be the point on y-axis which are at a distance  from point P. As Q is on y-axis it has the coordinates of form (0, y, 0).

=> ${\left(0-3\right)}^2+{\left(y+2\right)}^2+{\left(0-5\right)}^2$  = 25 x 2

=> 9 +  $y^2+2^2+2.y.2+25=50$

=> $y^2+4y+34+4-50=0$

=> $y^2+4y-12=0$

=> $y^2+6y-2y-12=0$

=> $y\left(y+6\right)-2\left(y+6\right)=0$

=> $\left(y+6\right)\left(y-2\right)=0$

=> $y=-6, y=2$

So the coordinates Q are (0, 2, 0) and (0, –6, 0).

<p><strong>18.&nbsp;</strong>Let Q be the point on y-axis which are at a distance &nbsp;from point P. As Q is on y-axis it has the coordinates of form (0, y, 0).</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1742460718phpp0E8Se_480x360.jpeg" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1742460718phpp0E8Se.jpeg" alt="" width="439" height="90"></picture></div><div><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1742460789phpVz3ZsQ_480x360.jpeg" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1742460789phpVz3ZsQ.jpeg" alt="" width="353" height="99"></picture></div><div><strong>=&gt; <span contenteditable="false"> <math><mrow><msup><mrow><mrow><mo>(</mo> <mrow><mn>0</mn> <mo>−</mo> <mn>3</mn></mrow> <mo>)</mo></mrow></mrow> <mrow><mn>2</mn></mrow></msup> <mo>+</mo> <msup><mrow><mrow><mo>(</mo> <mrow><mi>y</mi> <mo>+</mo> <mn>2</mn></mrow> <mo>)</mo></mrow></mrow> <mrow><mn>2</mn></mrow></msup> <mo>+</mo> <msup><mrow><mrow><mo>(</mo> <mrow><mn>0</mn> <mo>−</mo> <mn>5</mn></mrow> <mo>)</mo></mrow></mrow> <mrow><mn>2</mn></mrow></msup></mrow></math> </span>&nbsp;</strong>= 25 x 2</div><div><strong>=&gt; </strong>9 +<strong>&nbsp;</strong><span contenteditable="false"> <math> <mrow> <msup> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mn>2</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mo>.</mo> <mi>y</mi> <mo>.</mo> <mn>2</mn> <mo>+</mo> <mn>2</mn> <mn>5</mn> <mo>=</mo> <mn>5</mn> <mn>0</mn> </mrow> </math> </span></div><div><strong>=&gt; <span contenteditable="false"> <math> <mrow> <msup> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>4</mn> <mi>y</mi> <mo>+</mo> <mn>3</mn> <mn>4</mn> <mo>+</mo> <mn>4</mn> <mo>−</mo> <mn>5</mn> <mn>0</mn> <mo>=</mo> <mn>0</mn> </mrow> </math> </span></strong></div></div><p><strong>=&gt; <span contenteditable="false"> <math> <mrow> <msup> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>4</mn> <mi>y</mi> <mo>−</mo> <mn>1</mn> <mn>2</mn> <mo>=</mo> <mn>0</mn> </mrow> </math> </span></strong></p><p><strong>=&gt; <span contenteditable="false"> <math> <mrow> <msup> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>6</mn> <mi>y</mi> <mo>−</mo> <mn>2</mn> <mi>y</mi> <mo>−</mo> <mn>1</mn> <mn>2</mn> <mo>=</mo> <mn>0</mn> </mrow> </math> </span></strong></p><p><strong>=&gt; <span contenteditable="false"> <math> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mrow> <mi>y</mi> <mo>+</mo> <mn>6</mn> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <mi>y</mi> <mo>+</mo> <mn>6</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </math> </span></strong></p><p><strong>=&gt;</strong><span contenteditable="false"> <math> <mrow> <mrow> <mo>(</mo> <mrow> <mi>y</mi> <mo>+</mo> <mn>6</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mi>y</mi> <mo>−</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </math> </span></p></div></div><p>=&gt;&nbsp;<span title="Click to copy mathml"><math><mrow><mi>y</mi><mo>=</mo><mo>−</mo><mn>6</mn><mo>,</mo><mo>&nbsp;</mo><mi>y</mi><mo>=</mo><mn>2</mn></mrow></math></span></p><p>So the coordinates Q are (0, 2, 0) and (0, –6, 0).</p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment