Show that the line with equation 4y+3x=44 is a tangent to the circle with centre (5,1) and radius 5.
1 answer:
When a line is a tangent to a circle then the point of a tangent on a circle is perpendicular and also equal to the radius
So for perpendicular.
4y + 3x - 44 = 0
So, a = 4
b = 3
c = -44
x = 5
y = 1
Putting the values in the formula, we get
P = -4.2
Since the radius of the circle 5 is not equal to P, The line is not a tangent to the circle.
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One way to write a line is y=mx+b, where b is a number, m is the slope of the line, and y and x are variables that you can plug numbers into. We know that we have two points, (0,5) and (10,0). To find the slope of a line, we can use the equation
Plugging this in for our points, we get
as our slope (we get -1/2 by dividing both -5 and 10 by 5 from the previous fraction), making our equation y=(-1/2)x+b. Plugging a point in to find out what b is, we get 0=(-1/2)10+b=-5+b. Adding 5 to both sides to separate the b, we get 5=b, making our equation y=(-1/2)x+5. To find out what x is for (x,2), since the y value comes second, we can plug in 2 into our equation to get 2=(-1/2)x+5. Since we want to solve for x, we have to separate it. Subtracting 5 from both sides, we get -3=(-1/2)x. Since we can multiply -1/2 by its reciprocal (switching the numerator and denominator) to get 1 (and therefore x on the right sides as 1*x=x), we multiply both sides by -2 to get 6=x, making the point (6,2)
Feel free to ask further questions!
Plugging this in for our points, we get
Feel free to ask further questions!