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Conic Sections Ncert Solutions Maths class 11th Maths Class 11th

Let A(1, 4) and B(1, -5) be two points. Let P be a point on the circle ${(x - 1)}^{2} + {(y - 1)}^{2} = 1$ such that ${(P A)}^{2} + {(P B)}^{2}$ have a maximum value, then the points P, A and B lie on:

Option 1 -

An ellipse

Option 2 -

A straight line

Option 3 -

A parabola

Option 4 -

A hyperbola

2 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

$P A^{2} + P B^{2} = c o s^{2} θ + {(s i n θ - 3)}^{2} + c o s^{2} θ + {(s i n θ + 6)}^{2}$

= 2 cos² θ + 2 sin² θ + 6 sin q + 45

= 6 sin θ + 47

for maximum of PA² + PB², sin θ = 1

then P (1, 2)

Hence P, A & B will lie on a straight line.

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Slope of axis = $\frac{1}{2}$

$y - 3 = \frac{1}{2} (x - 2)$

⇒ 2y – 6 = x – 2

⇒ 2y – x – 4 = 0

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Let A(1, 4) and B(1, -5) be two points. Let P be a point on the circle ${(x - 1)}^{2} + {(y - 1)}^{2} = 1$ such that ${(P A)}^{2} + {(P B)}^{2}$ have a maximum value, then the points P, A and B lie on:

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Let A(1, 4) and B(1, -5) be two points. Let P be a point on the circle ( x − 1 ) 2 + ( y − 1 ) 2 = 1 such that ( P A ) 2 + ( P B ) 2 have a maximum value, then the points P, A and B lie on:

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Let A(1, 4) and B(1, -5) be two points. Let P be a point on the circle ${(x - 1)}^{2} + {(y - 1)}^{2} = 1$ such that ${(P A)}^{2} + {(P B)}^{2}$ have a maximum value, then the points P, A and B lie on: