Parametric form and focal chord

JEE Main Mathematics · Parabola · 17 questions, latest first

• Let O be the vertex of the parabola y^2=4 x and its chords OP and OQ are perpendicular to each other. If the locus of the…20268 April, Shift 2 · Q11
• Let chord PQ of length 3 √13 of the parabola y^2=12 x be such that the ordinates of points P and Q are in the ratio 1: 2. If the…20266 April, Shift 1 · Q12
• Let the directrix of the parabola P: y^2=8 x, cut x -axis at the point A. Let B(α, β), α>1, be a point on P such that the slope…20265 April, Shift 2 · Q12
• Let A, B and C be the vertices of a variable right angled triangle inscribed in the parabola y^2=16 x. Let the vertex B…20264 April, Shift 2 · Q24
• If the chord joining the points P_1(x_1, y_1) and P_2(x_2, y_2) on the parabola y^2=12 x subtends a right angle at the vertex of…202622 January, Shift 1 · Q10
• Let one end of a focal chord of the parabola y^2=16 x be (16,16). If P(α, β) divides this focal chord internally in the ratio 5:…202621 January, Shift 2 · Q11
• Let y^2=12 x be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the x -axis such that ∠…202621 January, Shift 2 · Q12
• Let the point P of the focal chord PQ of the parabola y^2=16 x be (1,-4). If the focus of the parabola divides the chord PQ in…20252 April, Shift 2 · Q11
• Let the focal chord PQ of the parabola y^2=4 x make an angle of 60^° with the positive x axis, where P lies in the first…20252 April, Shift 1 · Q1
• Let y^2=12 x be the parabola and S be its focus. Let PQ be a focal chord of the parabola such that (SP)(SQ)=147/4. Let C be the…202529 January, Shift 2 · Q23
• Let ABCD be a trapezium whose vertices lie on the parabola y^2=4 x. Let the sides AD and BC of the trapezium be parallel to y…202528 January, Shift 1 · Q10
• Let P(4,4 √3) be a point on the parabola y^2=4 ax and PQ be a focal chord of the parabola. If M and N are the foot of…202522 January, Shift 2 · Q10
• Let A, B and C be three points on the parabola y^2=6 x and let the line segment A B meet the line L through C parallel to the x…20249 April, Shift 2 · Q28
• Suppose AB is a focal chord of the parabola y^2=12 x of length l and slope m<√3. If the distance of the chord AB from the origin…20245 April, Shift 1 · Q28
• Let the length of the focal chord PQ of the parabola y^2=12 x be 15 units. If the distance of PQ from the origin is p, then 10…20244 April, Shift 1 · Q28
• Let PQ be a focal chord of the parabola y^2=36 x of length 100, making an acute angle with the positive x -axis. Let the ordinate…202313 April, Shift 1 · Q16
• If the x -intercept of a focal chord of the parabola y^2=8 x+4 y+4 is 3, then the length of this chord is equal to ____.20231 February, Shift 2 · Q88