Prove algebraically that the straight line with equation x - 2y = 10 is a tangent to the circle with equation x^2 + y^2= 20
rearrange line equation: x=10 + 2ysubstitute into circle equation: (10+2y)2 + y2=20expand: 4y2 +20y +20y + 100 + y2= 20 collect terms: 5y2 + 40y +100 = 20move all to one side: 5y2 + 40y + 80=0divide by 5: y2 + 8y + 16=0factorise: can use quadratic equation but this one is easy to spot:(y+4)2 =0therefore they meet at y= -4x= 10 + 2(-4) =2line meets the circle at (2, -4)as there is only one point of intersection, it is therefore a tangent
AB
Related Maths GCSE answers
All answers ▸What is the nth term of the sequence 5, 7, 9, 11....
Solve x² - 3x - 2 = 0
work out the area of a trapezium where the height is 4mm, the top length is 8mm and the bottom length is 12.5mm
In an office there are twice as many females as males. 1/4 of the females wear glasses. 3/8 of the males wear glasses. 84 people in the office wear glasses. Work out the number of people in the office.