Year 12s: what will be the first way you research your future options? >>

circles and tangents..? help?

just wondering if anyone can help me....

1) FIND THE EQUATIONS TO THE TANGENTS TO THE CIRCLE

x^2 + y^2 = 25

FROM THE POINT P(2,11), OUTSIDE THE CIRCLE

and...

2) SHOW THAT THE STRAIGHT LINE

x - 3y - 10 = 0

IS A TANGENT TO THE CIRCLE

x^2 + y^2 = 10

BY: (I) FINDING THE DISTANCE OF THE LINE FROM THE ORIGIN
(II) SHOWING THAT THE LINE MEETS THE CIRCLE AT ONE POINT ONLY

FURTHER, DETERMINE THE EQUATION TO THE NORMAL TO THE CIRCLE THROUGH THE POINT OF CONTACT OF THE TANGENT

got really stuck...thanks for any help :smile:

Reply 1

CCDB

ooh and particularly the first one...im really stuck :frown:

Reply 2

Chaoslord

CCDB

just wondering if anyone can help me....

1) FIND THE EQUATIONS TO THE TANGENTS TO THE CIRCLE

x^2 + y^2 = 25

FROM THE POINT P(2,11), OUTSIDE THE CIRCLE

you should know

\frac{dy}{dx}

givens you the gradients of the tangents to the curve, so using implicit differentiation (let me know if you need me to explain this concept, i'll assume you know it already to save time):

[spoiler]

2x + 2y\frac{dy}{dx} = 0

2y\frac{dy}{dx} = -2x

\frac{dy}{dx} = \frac{-2x}{2y}

\frac{dy}{dx} = \frac{-x}{y}

subbing in the values

x = 2

and

y = 11

you get

\frac{dy}{dx} = \frac{-2}{11}

now using the formula

y - y_1 = m(x - x_1)

to find an equation of a line we get

y - 11 = \frac{-2}{11}(x - 2)

y = \frac{-2x}{11} + \frac{4}{11} + 11

\therefore y = \frac{-2x}{11} + \frac{125}{11}

11y + 2x - 125 = 0[br][br]

Reply 3

Chaoslord

CCDB

2) SHOW THAT THE STRAIGHT LINE

x - 3y - 10 = 0

IS A TANGENT TO THE CIRCLE

x^2 + y^2 = 10

BY: (I) FINDING THE DISTANCE OF THE LINE FROM THE ORIGIN
(II) SHOWING THAT THE LINE MEETS THE CIRCLE AT ONE POINT ONLY

FURTHER, DETERMINE THE EQUATION TO THE NORMAL TO THE CIRCLE THROUGH THE POINT OF CONTACT OF THE TANGENT

part i

Spoiler

part ii

Spoiler

Latest

Articles for you

What university is really like

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers

Why I chose a law degree and what studying law was like

circles and tangents..? help?

Related discussions

Latest

Trending

Trending

Articles for you