Let <math><mi>x</mi><mo>=</mo><mn>4</mn></math> be a directrix to an ellipse whose centre is at the origin and its eccentricity is <math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac></math> . If <math><mi>P</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>β</mi><mo>)</mo><mo>,</mo><mi>β</mi><mo>></mo><mn>0</mn></math> is a point on this ellipse, then the equation of the normal to it at <math><mi>P</mi></math> is:

[x]2+2 [x+2]-7=0⇒ [x]2+2 [x]+4-7=0⇒ [x]=1, -3⇒x∈ [1,2)∪ [-3, -2)

Let&nbsp;<math><mi>x</mi><mo>=</mo><mn>4</mn></math>&nbsp;be a directrix to an ellipse whose centre is at the origin and its eccentricity is&nbsp;<math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac></math>&nbsp;. If&nbsp;<math><mi>P</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>β</mi><mo>)</mo><mo>,</mo><mi>β</mi><mo>&gt;</mo><mn>0</mn></math>&nbsp;is a point on this ellipse, then the equation of the normal to it at&nbsp;<math><mi>P</mi></math>&nbsp;is:

Ask & Answer Question

Option 1 -

$4 x - 2 y = 1$

Option 2 -

$4 x - 3 y = 2$

Option 3 -

$7 x - 4 y = 1$

Option 4 -

$8 x - 2 y = 5$

3 Views | Posted 2 months ago

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

$[x]^{2} + 2 [x + 2] - 7 = 0$

$\begin{array}{r} \Rightarrow [x]^{2} + 2 [x] + 4 - 7 = 0 \\ \Rightarrow [x] = 1, - 3 \\ \Rightarrow x \in [1,2) \cup [- 3, - 2) \end{array}$