If b,k are the intercepts of a focal chord of the parabola y2=4ax ,then k is equal to _____ - Maths - Conic Sections

Question

If b,k are the intercepts of a focal chord of the parabola
y2=4ax ,then k is equal to _____

Lovina Kansal · Accepted Answer

Dear student
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If coordinates of one end of focal chord are P(at2,2at) then the coordinates of other end will be Q=at2,-2at∴SP=at2-a2+2at-02=a2t4+a2-2a2t2+4a2t2=a2t4+a2+2a2t2=at2+a2=at2+a=at2+1=b  (given)    
(1)and SQ=at2-a2+-2at-02=a2t4+a2-2a2t2+4a2t2=a2t4+a2+2a2t2=at2+a2=at2+a=a1t2+1=k    (given)     
(2)Dividing (1) by (2), we getbk=at2+1a1t2+1⇒bk=t2+11+t2t2⇒bk=t2Putting in (1), we getat2+1=b⇒abk+1=b⇒bk+1=ba⇒k=abb-a
Regards