0

Guest

Courses New

show that all the chords of the curve 3x²-y²-2x+4y=0 which subtend a right angle at the origin pass through a fixed point

show that all the chords of the curve 3x²-y²-2x+4y=0 which subtend a right angle at the origin pass through a fixed point

Grade:12

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
5 years ago
Let (x,y) be a common point of chord y=mx+c, y=kx & 3x²−y²−2x+4y=0

First two give x & y which can be used in third to give (3−k²)c + (4k−2)(k−m) = 0

As a quadratic in k this is k²(4−c)−2k(2m+1)+(2m+3c) = 0

If the two values of k arising from this give perp lines thro O then (2m+3c)/(4−c) = −1

→ 2m+3c = −4+c → c=−m−2

Chord is thus y = mx–m−2 → y+2 = m(x−1) which always contains (1,−2)

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Analytical Geometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More