Shortest Distance Between Lines and Ellipse Relation
❓ Question Let the values of π , for which the shortest distance between the lines π₯ + 1 3 = π¦ 4 = π§ 5 and π ⃗ = ( π π ^ + 2 π ^ + π ^ ) +…
Conic Sections
Focus–Latus Rectum Property in Hyperbola
❓ Concept Hyperbola dikhe, focus dikhe, aur latus rectum right angle subtend kar raha ho? π Samajh jao — geometry ka gold mine mil chuka hai ?…
Hyperbola Latus Rectum Right Angle Problem
❓ Question Consider the hyperbola x 2 a 2 − y 2 b 2 = 1 \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 having one of its foci at P ( − 3 , 0 ) . P(-3,\,0).…
Derive Parabola Equation from Focus and Directrix
❓ Concept Parabola ka equation yaad nahi? π Koi tension nahi! Bas focus–directrix definition yaad rakho — aur poora parabola khud-ba-khud ban…
Parabola from Focus and Directrix
❓ Question Let P P be the parabola whose focus is ( − 2 , 1 ) (-2,\,1) and whose directrix is 2 x + y + 2 = 0. 2x + y + 2 = 0. Find the sum…
Find Product of Focal Distances Hyperbola
❓ Question Let a hyperbola in standard form have transverse and conjugate axes of lengths 2 a 2a and 2 b 2b , respectively. One focus is at ( − 5 …