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Find the equations of the tangents to the curve x² + y2 – 2x – 4y + 1 = 0, which areparallel to the X-axis.ution: |
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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=2When y=2x2+22−2x−4(2)+1=0 ⇒x2+4−2x−8+1=0⇒x2−2x−3=0 ⇒(x−1)(x−3)=0 ⇒x=−1 or 3So, the points where tangents are parallel to y− axis =(−1,2),(3,2)Step-by-step EXPLANATION: |
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