Question

At what points on the curvexa-y=2 the slopes
of tangents are equal to 2?​

Answer 1

Step-by-step explanation:

So this simply implies that when the curve passes through x-axis the y-coordinate should be zero so we have

x2+xy+y2=7

x2+0x+0=7

x=sqrt(7)

So we have 2 values

x= +(7^1/2) , -( 7^1/2)

For tangents we have slope of tangent is given by dy/dx of the curve at that point

d/dx(x2+xy+y2=7)

2x+y+xdy/dx+2ydy/dx=0

Since we have slopes for y=0

We have 2x + xdy/dx=0

Since x is not equal to zero we have

2x=-x dy/dx

Thus dy/dx =-2

Hence for any point on the curve x2+xy+y2=7

At y=0 the slope of tangent is - 2

Hence both the tangents we get have same slope and thus they are parallel..