A Level maths help needed!!!
Show that the line y=3x-10 is a tangent to the circle x2+y2=10
To show a line is a tangent to a circle, show one of two things:
1. A point of intersection
2. Show the distance from the centre of the circle to the tangent is r.
One easy way it to substitute the line in to the circle. Make the straight line equal to y & x, and then plug in to the equation of the circle respectively.
1. A point of intersection
2. Show the distance from the centre of the circle to the tangent is r.
One easy way it to substitute the line in to the circle. Make the straight line equal to y & x, and then plug in to the equation of the circle respectively.
Original post by CameronWS
To show a line is a tangent to a circle, show one of two things:
1. A point of intersection
2. Show the distance from the centre of the circle to the tangent is r.
One easy way it to substitute the line in to the circle. Make the straight line equal to y & x, and then plug in to the equation of the circle respectivel
1. A point of intersection
2. Show the distance from the centre of the circle to the tangent is r.
One easy way it to substitute the line in to the circle. Make the straight line equal to y & x, and then plug in to the equation of the circle respectivel
After I substitute the straight line equation into the circle equation how do I 'show' that y=3x-10 is a tangent
Original post by Juliakinga
After I substitute the straight line equation into the circle equation how do I 'show' that y=3x-10 is a tangent
Well if it's a tangent it has one point of intersection, by substituting in for x and y. You're finding that one point hence proving it's a tangent. We know it's a linear/straight too.
Original post by Juliakinga
After I substitute the straight line equation into the circle equation how do I 'show' that y=3x-10 is a tangent
By proving there is a single solution to the leftover quadratic
Original post by Juliakinga
After I substitute the straight line equation into the circle equation how do I 'show' that y=3x-10 is a tangent
How do we show a quadratic equation has two equal roots without solving it?
Would you use the quadratic equation?
Original post by RDKGames
By proving there is a single solution to the leftover quadratic
Thank you
Original post by CameronWS
Well if it's a tangent it has one point of intersection, by substituting in for x and y. You're finding that one point hence proving it's a tangent. We know it's a linear/straight too.
Ahh okay, I understand
solve the system of simultaneous equations. Now if the line is not tangent, it either does not intersect or intersects twice. So there should only be one unique solution for the equation.
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