SATHEE: Parabola 1 Question 7

Parabola 1 Question 7

7. Axis of a parabola is $y = x$ and vertex and focus are at a distance $\sqrt{2}$ and $2 \sqrt{2}$ respectively from the origin. Then, equation of the parabola is

(2006, 3M)

(a) $(x - y)^{2} = 8 (x + y - 2)$

(b) $(x + y)^{2} = 2 (x + y - 2)$

(d) $(x + y)^{2} = 2 (x - y + 2)$

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Answer:

Correct Answer: 7. (a)

Solution:

Since, distance of vertex from origin is $\sqrt{2}$ and focus is $2 \sqrt{2}$ .

$∴ V (1, 1)$ and $F (2, 2)$ (i.e. lying on $y = x$ )

where, length of latusrectum

$= 4 a = 4 \sqrt{2} [∵ a = \sqrt{2}]$

$∴$ By definition of parabola

where, $P N$ is length of perpendicular upon $x + y - 2 = 0$ , i.e. tangent at vertex

$\begin{array}{ll} \Rightarrow & \frac{(x - y)^{2}}{2} = 4 \sqrt{2} \frac{x + y - 2}{\sqrt{2}} \\ \Rightarrow & (x - y)^{2} = 8 (x + y - 2) \end{array}$

Parabola 1 Question 7

7. Axis of a parabola is $y = x$ and vertex and focus are at a distance $\sqrt{2}$ and $2 \sqrt{2}$ respectively from the origin. Then, equation of the parabola is

Answer:

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Parabola 1 Question 7

7. Axis of a parabola is y=x and vertex and focus are at a distance 2 and 22 respectively from the origin. Then, equation of the parabola is

Answer:

Engineering Preparation

Medical Preparation

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Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

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NCERT Exercise Video Solution

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7. Axis of a parabola is $y = x$ and vertex and focus are at a distance $\sqrt{2}$ and $2 \sqrt{2}$ respectively from the origin. Then, equation of the parabola is