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Topic: **How to write an equation perpendicular to a given point****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

May 22, 2019 / By Cimone

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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Did you like the answer? We found more questions related to the topic: **How to write an equation perpendicular to a given point**

well if Ryan, John and Susan share £165 in the ratio of 1:4:6, then £165 = 11 units (units referring to the value of the ratio, 1+4+6) . Then for each unit, there is £15. Therefore, Ryan: 1 unit = £15 John: 4 units = 4 * £15 = £60 Susan: 6 units = 6 * £15 = £90 <-- Answer to check if its right sum all their money and it should be £165 Answer for the second question: A year ago Pauls pet terrapin was 13.4 centermeters long the terrapin is now 6.25% longer. How long is it now? In here, you have to let 13.4 centimeters to be the 100% of the pet terrapin's length a year ago. When a year has passed, it grew 6.25 % longer, which means that it is 106.25% long in the sense of a year ago. Ok, so you know 100% = 13.4 centimeters 6.25 % means (13.4 * 6.25 / 100) since 1% = 1/100 this value (6.25%) gives 0.8375 centimeters adding this value to its length a year ago you get ( 13.4 + 0.8375 ) centimeters = 14.2375 centimeters This is how long it is now

If the ratio is 1:4:6, that's 11 parts total. So Susan gets 6 parts of the 11. Set up a ratio: 6/11 = n/165 11n = 990 n = 90 She gets £90. If the terrapin increased by 6.25%, he's now 106.25% of what he was, so: 13.4 * 1.0625 = 14.2375 cm long

Susan receives 6/(1+4+6)*165=6/11*(165)=90 Second one is: 13.4+(13.4*(6.25/100)) =13.4(1.0625) =14.2375 cm

i) there will be infinite such circles. If it was meant to be the center of the circle, the answer would be x^2 + y^2 - 4x + 6y - 12 = 0 ii) (x+2)^2 + (y+3)^2 = (sqrt(38))^2 iii) a) 5 b) 4x+3y-19=0 c) arctan(7)

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Aha. Basic math is basic. Anyhoo, you have to set up a proportion like so: 28/x (x being the price before the discount) = 80/100 (80/100 being the percentage that 28 is of the previous number.) Then, you can perform cross multiplication and multiply 28*100, then divide by 80. That should give you the amount of money it cost. That's the way I do it in math class, anyway. I dunno if our currency difference would change the answer or not, though.

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