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x^2+y^4=10x+7 @ (1,-2)
Rearrange to isolate y.
y=(-x^2+10x+7)^(1/4)
Take derivative.
y'=(1/4)*((-x^2+10x+7)^(-3/4))*(-2x+10)
y'=(-2x+10)/4*(-x^2+10x+7)^(3/4)
Sub in x=1.
y'=8/2*(16)^(3/4)
y'=2/8
y'=1/4
y'=m=slope=1/4
Sub m and (1,-2) into linear equation (tangent line).
m*(x-x1)=y-y2
(1/4)(x-1)=y+2
Isolate y.
Equation of tangent line: y=(1/4)x-(9/4).
The third question is unclear.
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How many ways can an arc be tangent to 2 lines?
Although normally it is the line that is considered to be tangent to an arc, an arc can be tangent to infinitely many lines and so the answer to the question is: in infinitely many ways.
Difference between tangent and parallel lines?
parallel lines never touch, never get any closer or any further apart. tangent lines touch at one point
What is the differential equation of the family of straight lines y equals mx?
dy/dx = m
How many lines are tangent to a circle?
You can have a tangent line for every point on a circle, so the answer is theoretically infinite.
Is y equals -3x plus 3 and 4y plus x equals -1 perpendicular lines?
No because the slope of the second equation is 1/4 and for it to be perpendicular to the first equation it should be 1/3
Do straight lines have tangent?
no
What is the vertex of the equation y equals 2x-1?
3
Which of the lines below is the graph of the equation y equals x plus 1?
answer is 1
How many ways can an arc be tangent to 2 lines?
Although normally it is the line that is considered to be tangent to an arc, an arc can be tangent to infinitely many lines and so the answer to the question is: in infinitely many ways.
Difference between tangent and parallel lines?
parallel lines never touch, never get any closer or any further apart. tangent lines touch at one point
What is the differential equation of the family of straight lines y equals mx?
dy/dx = m
What is a theorem about two lines tangent to a circle at the endpoints of a diameter?
Two lines tangent to a circle at the endpoints of its diameter are parallel. See related link for proof.
How many lines are tangent to a circle?
You can have a tangent line for every point on a circle, so the answer is theoretically infinite.
What equation represents a line that is parallel to the line reprensented by the equation y equals -2 plus 5?
I assume the question should be y = -2x + 5? The equation of a line that is parallel to that line is any line that begins 7 = -2x ... after the -2x any number may be added or subtracted. Parallel lines have the same slope. In the original equation, the slope is -2.
Is the equation 32x-4 equals -18 equivalent to 6x-12 equals -18?
No. In the coordinate plane, for example, they would result in different lines.
Is y equals -3x plus 3 and 4y plus x equals -1 perpendicular lines?
No because the slope of the second equation is 1/4 and for it to be perpendicular to the first equation it should be 1/3
Difference between secant lines and tangent lines?
A secant line touches a circle at two points. On the other hand a tangent line meets a circle at one point.
