Question

Find the equations of the tangents to the
curve x² + y2 – 2x – 4y + 1 = 0, which are
parallel to the X-axis.
ution:​

Answer 1

Answer:

x2+y2−2x−4y+1

⇒2x+2ydxdy​−2−4dxdy​=0⇒x+ydxdy​−1−2dxdy​=0 ⇒ (y−2)dxdy​=(1−x)dxdy​=(1−x)(y−2)​

for the tangents to be parallel to y− axis, dxdy​=0

∴dxdy​=(1−x)(y−2)​=0 ⇒y=2

When y=2

x2+22−2x−4(2)+1=0 ⇒x2+4−2x−8+1=0⇒x2−2x−3=0 ⇒(x−1)(x−3)=0 ⇒x=−1 or 3

So, the points where tangents are parallel to y− axis

=(−1,2),(3,2)

Step-by-step explanation: