Falling Behind in Studies? Join Our Performance Improvement Batch. Enroll For Free
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Live 1-1 coding classes to unleash the creator in your Child
if pair of lines ax^2+2hxy+by^2+2gx+2fy+c=0 intersect on y axis then ... a.2fgh=hg^2+ch^2 b.hg^2 not equal to ch^2 c.abc=2fgh d.none of these
A pair of equations intersecting on the y-axis is given by:(px+my+n)(qx+my+n)=0. You can see that by putting x=0 in each factor on the LHS, and observing that the y-coordinate is the same. Expanding and equating the coefficients of x^2, xy, etc in the given expression, we havea=pq, 2h=m(p+q), b=m^2, 2g=n(p+q), f=mn and c=n^2.Now the reference cited below proves the general condition for a second-degree equation to represent a pair of straight lines as:af^2 + bg^2 + ch^2 = 2fgh + abc (You can go through the proof if you wish)Using our results, af^2 =pqm^2n^2 = abc. Thus af^2 and abc cancel out from the general condition, and we're left with bg^2 + ch^2 = 2fgh, which is what we're asked to prove.ThanksBharat BajajIIT Delhiaskiitians faculty
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -