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 )
Find the equations of the chords of the parabola y2 = 4ax which pass through the point (-6a, 0) and which subtends an angle of 45° at the vertex.
The vertex of parabolay^2 = 4axis (0,0). Equation of a chord in the slope-intercept form isy=kx+b (1)Here k=tan 45°=1, because a chord subtends an angle of 45° at the vertex.So, in fact (1) is given byy=x+b (2)On the other hand, this line passes through the point (–6a, 0), consequently its coordinates satisfy equation(2):0=-6a+b,b=6a.Finally, y=x+6a is the equation of chord.Answer: y=x+6a.
The vertex of parabola y2=tax is O (0,0)Equation of the chord isy-y1=m (x-x1)The chord passes through point (-6a,0)Thus point should satisfy the eqn of chord y=m (x+6a)Now ,y2=4ax (y-mx)/(6ma)-eq1Since , (y-mx)/6ma=1Now slove the equation 1you will getm1+m2=2/3m m1m2=2/3We know that, tan (A)=|m1-m2|/|1+m1m2|Solve that by squaring and you will get ,m=+2/7,-2/7The equation of chord will be 1]y=2/7 (x+6a) 2]y=-2/7 (x+6a)
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -