Question

Find the equations of tangents to the circle x2 + y2 = 10 at the
points whose abscissa is 1.​

Answer 1

Step-by-step explanation:

abscissa=1

x=1

x^2+y^2=10

1^2+y^2=10

y^2=10-1

y=sqrt.9

y=+-3

the tangents are y=3 and y= -3 lines

Answer 2

x²+y² = 10 equation of Circle

if abscissa is 1 then

(1)²+(y)²= 10

y² = 9

y = +-3

x²+y² = 10 (D.w.r to x)

d(x²+y²)/dx = d(10)/dx

2x + 2ydy/dx = 0

dy/dx = -2x/2y = -2(1)/2*3 = -1/3 or -2(1)/2*(-3)= 1/3

equation of tangent is y-y1 = m(x-x1)

(x1, y1 ) = (1,+3) or (1,-3)

so (1) equation point (1,3) when m = 1/3

y- 3 = 1/3(x-1)

3y-9 = x-1

3y -x -9+1 = 0

3y-x-8 = 0

equation (2) , when point (1,3) and m = -1/3

y - (3) = -1/3(x-1)

(y -3 )*3 =- x+1

3y - 9 = -x+1

3y +x-10

equation (3) when point (1,-3) and m = 1/3

y +3= 1/3(x-1)

3y+9 = x-1

3y-x+10

equation (4) when point (1,3) and m = -1/3

y-3 = -1/3(x-1)

3y-9 = -x+1

3y +x -10

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Hope it's helpful