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# Help with maths question please?

Topic: How to write an equation perpendicular to a given point
May 22, 2019 / By Cimone
Question: could someone please explain to me how you solve these 3 questions ii. Find the equation of the circle passing through (-2, 3) with radius 5 iii. Write in centre-radius form the following circle. x^2 + y^2 + 4x + 6y – 25 = 0 3. The points A(-1,3), B(3,0) and C(1,5) are on a graph i. find the distance between A and B ii. an equation of the line through C which is perpendicular to AB iii. angle CAB thank you

Bab | 4 days ago
ii. There could be a lot of circles passing through the point (-2,3) with radius 5. If you mean (-2,3) as the centre, then it's simpler. All circle equations follow the form: (x-a)²+(y-b)²=r² with a and b as the x and y coordinates of the centre respectively and r as the radius So if we substitute the values: (x-(-2))²+(y-(3))²=5² => (x+2)²+(y-3)²=5² iii. This is simple completing the square and then simplifying into the form (x-a)²+(y-b)²=r² So rearranged to make it easier: x²+4x+y²+6y-25=0 And completing the square: (x+2)²-4+(y+3)²-9-25=0 =>(x+2)²+(y+3)²=38 3.i. To find the distance, pythagoras' theorem must be used. That is: a²+b²=c² We use the coordinates to give us values of a and b to make a triange where c=AB So a²=(3-(-1))²=(3+1)²=4²=16 and b²=(3-0)²=3²=9 Therefore: 16+9=AB² => 25=AB² => AB=5 3.ii. This is a bit trickier. First, we need to find the gradient of the line AB Gradient=(change in y)/(change in x) (3--1)/(0-3)=4/-3 To find the perpendicular gradient: Gradient AB * Gradient perpendicular = -1 So gradient perpendicular = 3/4 Now to find the equation, we must use the form: y=mx+c and use the co ordinates of C as our values of y and x and our gradient as m Therefore: 5=3/4(1)+c =>20/4=3/4+17/4 Therefore, putting back into the general form: y=3/4x+17/4 Usually they want it in a simpler form with integers so: 4y=3x+17 3.iii. If we substitute the coordinates of A into the equation we found above: 4(3)=3(-1)+17 =>12=-3+17 =>12=12 Which means A is a point on the line. If the line AC is perpendicular to line AB, the angle at A (angle CAB) will be 90° (That took me a really long time to type out :S) I hope I helped :):)
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