EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>Exercise 1>Q 143

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Let the line $x + y = 1$ meet the circle $x^{2} + y^{2} = 4$ at the points $A$ and $B$ . If the line perpendicular to $A B$ and passing through the midpoint of the chord $A B$ intersects the circle at $C$ and $D$ , then the area of the quadrilateral $A D B C$ is equal to

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Important Questions on Point and Straight Line

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JEE Main

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>Exercise 1>Q 144

Let $A B C$ be a triangle formed by the lines $7 x - 6 y + 3 = 0, x + 2 y - 31 = 0$ and $9 x - 2 y - 19 = 0$ . Let the point $(h, k)$ be the image of the centroid of $∆ A B C$ in the line $3 x + 6 y - 53 = 0$ . Then $h^{2} + k^{2} + h k$ is equal to

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>Exercise 1>Q 145

Let A, B, C be three points in xy - plane, whose position vector are given by \sqrt{3} \hat{i} + \hat{j}, \hat{i} + \sqrt{3} \hat{j} and a \hat{i} + (1 - a) \hat{j} respectively with respect to the origin O . If the distance of the point C from the line bisecting the angle between the vectors \vec{OA} and \vec{OB} is \frac{9}{\sqrt{2}}, then the sum of all the possible values of a is :

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>Exercise 1>Q 146

Two equal sides of an isosceles triangle are along - x + 2 y = 4 andx + y = 4 . If m is the slope of its third side, then the sum, of all possible distinct values of m, is :

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>Exercise 1>Q 147

If A and B are the points of intersection of the circle x^{2} + y^{2} - 8 x = 0 and the hyperbola \frac{x^{2}}{9} - \frac{y^{2}}{4} = 1 and a point P moves on the line 2 x - 3 y + 4 = 0, then the centroid of ∆ PAB lies on the line :