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Straight Lines and Pair of Straight Lines

11 questions · Mathematics · JEE Advanced

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JEE Advanced
Mathematics
Straight Lines and Pair of Straight Lines

Straight Lines and Pair of Straight Lines

11 questions · Mathematics · JEE Advanced

Let S denote the locus of the point of intersection of the pair of lines $4 x - 3 y = 12 α$ , $4 α x + 3 α y = 12$ , where $α$ varies over the set of non-zero real numbers. Let T be the tangent to S passing through the points $(p, 0)$ …2025 · Shift 2 · Q20 · MCQ
Consider the lines L1 and L2 defined by $L_{1} : x 2 + y - 1 = 0$ and $L_{2} : x 2 - y + 1 = 0$ For a fixed constant $λ$ , let C be the locus of a point P such that the product of the distance of P from L1 and the distance of P…2021 · Shift 1 · Q28 · Numerical
Consider the lines L1 and L2 defined by $L_{1} : x 2 + y - 1 = 0$ and $L_{2} : x 2 - y + 1 = 0$ For a fixed constant $λ$ , let C be the locus of a point P such that the product of the distance of P from L1 and the distance of P…2021 · Shift 1 · Q29 · Numerical
For a point $P$ in the plane, Let $d_{1} (P)$ and $d_{2} (P)$ be the distance of the point $P$ from the lines $x - y = 0$ and $x + y = 0$ respectively. The area of the region $R$ consisting of all points $P$ …2014 · Shift 1 · Q25 · Numerical
For $a > b > c > 0,$ the distance between $(1, 1)$ and the point of intersection of the lines $a x + b y + c = 0$ and $b x + a y + c = 0$ is less than $(22)$ . Then2013 · Shift 1 · Q29 · MCQ
A straight line $L$ through the point $(3, - 2)$ is inclined at an angle $6 0^{\circ}$ to the line $3 x + y = 1.$ If $L$ also intersects the x-axis, then the equation of $L$ is2011 · Shift 1 · Q30 · MCQ
A straight line through the vertex p of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then :2008 · Shift 1 · Q37 · Multiple correct
Let a and b be non-zero real numbers. Then, the equation $(a x^{2} + b y^{2} + c) (x^{2} - 5 x y + 6 y^{2}) = 0$ represents :2008 · Shift 1 · Q43 · MCQ
Consider three points $P = (- sin (β - α), - cos β), Q = (cos (β - α), sin β)$ and $R = (cos (β - α + θ), sin (β - θ))$ where $0 < α, β, θ < \frac{π}{4}$ . Then :2008 · Shift 2 · Q41 · MCQ
Consider the lines given by: $L_{1} : x + 3 y - 5 = 0$ $L_{2} : 3 x - k y - 1 = 0$ $L_{3} : 5 x + 2 y - 12 = 0$ Match the Statement/Expressions in Column I with the Statements/Expressions in Column II. Includes table2008 · Shift 2 · Q43 · MCQ
Consider the following linear equations $a x + b y + cz = 0$ $b x + cy + a z = 0$ $c x + a y + b z = 0$ Match the conditions/expressions in Column I with statements in Column II. Includes table2007 · Shift 1 · Q42 · MCQ