Please help Q51 The equation of the chords of length 5 and passing through the point (3, 4) - Maths -

Question

Please help

Q51 The equation of the chords of length 5 and passing through the
point (3, 4) on the circle 4x2 + 4y2 –
24x – 7y = 0 are

(a) 4x + 3y = 0 (b) 4x – 3y = 0

(c) 4x + 3y – 24 = 0 (d) 4x + 3y – 12 = 0

Aarushi Mishra · Accepted Answer

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5a3b4fb29435f%20png"
style="width: 1022px; height: 720px;">
C:x2+y2-6x-74y=0Centre of the circle C=(-g,-f)C=3,78radius of cricle r=g2+f2-cr=9+4964-0r=576+498=6258=258Using that perpendicular from center to a chord bisects itAD=52Using pythagoras theorem in ∆ADCr2=AD2+d2d2=r2-AD2=62564-254=625-40064=12564d=158Equaation of line passing through P(3,4) with slope m(y-4)=m(x-3)y=mx+4-3mmx-y+4-3m=0This line is at a distance of158 from C158=3m-78+4-3m1+m2158=258×11+m21+m2=259m2=169m=±43Equation can be43x-y+4-4=04x-3y=0or-43x-y+4+4=0-4x-3y+24=04x+3y-24=0

Please help Q51. The equation of the chords of length 5 and passing through the point (3, 4) on the circle 4x2 + 4y2 – 24x – 7y = 0 are (a) 4x + 3y = 0 (b) 4x – 3y = 0 (c) 4x + 3y – 24 = 0 (d) 4x + 3y – 12 = 0

Please help

Q51. The equation of the chords of length 5 and passing through the point (3, 4) on the circle 4x² + 4y² – 24x – 7y = 0 are

(a) 4x + 3y = 0 (b) 4x – 3y = 0

(c) 4x + 3y – 24 = 0 (d) 4x + 3y – 12 = 0