Why isn't the answer to TMUA-P1X-MM3-03 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1X-MM3-03 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1X-MM3-03?

No — calculators are banned in the TMUA. TMUA-P1X-MM3-03 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1X-MM3-03?

TMUA-P1X-MM3-03 is Paper P1 · Coordinate geometry in the (x,y)-plane (specification code MM3), level 2. Drill more of the same topic from this page.

TMUA-P1X-MM3-03 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 2

P1MM3Level 2~180s target

Spec: MM3 · No calculator · ~180s

The circle

x^2 + y^2 = 25

passes through

P(3, 4)

. Find the equation of the tangent to the circle at

P

Options

$3x + 4y = 25$
$4x - 3y = 0$
$3x - 4y = -7$
$4x + 3y = 24$
$x + y = 7$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: tangent-perpendicular-radius, reciprocal-sign. Name the trap first, work the stem by hand, then open the solution below.

Show solution

The radius

OP

has gradient

\frac{4}{3}

, so the tangent has gradient

-\frac{3}{4}

y - 4 = -\frac{3}{4}(x - 3)

gives

3x + 4y = 25

. Trap:

4x - 3y = 0

is the radius line through

O

and

P

— plausible if you use the radius gradient instead of the perpendicular one.

Keep practising

Same topic · same level
P1MM3Level 2
TMUA-P1-MM3-001
In an arithmetic sequence the 3rd term is 11 and the 8th term is 31. What is the first term?
Coordinate geometry in the (x,y)-plane
Open TMUA-P1-MM3-001 →
Same trap: tangent-perpendicular-radius
P1MM3Level 2
TMUA-P1-MM3-009
A circle has centre O(0, 0) and the point P(6, 4) lies on it. Find the equation of the tangent to the circle at P.
Coordinate geometry in the (x,y)-plane
Open TMUA-P1-MM3-009 →
Step up a level
P1MM3Level 3
TMUA-P1-MM3-010
The line y = x + 1 crosses the circle x^2 + y^2 = 25 at two points. What is the length of the chord joining them?
Coordinate geometry in the (x,y)-plane
Open TMUA-P1-MM3-010 →

Browse more

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Keep practising

Same topic · same level

P1MM3Level 2

TMUA-P1-MM3-001

In an arithmetic sequence the 3rd term is 11 and the 8th term is 31. What is the first term?

Coordinate geometry in the (x,y)-plane

Open TMUA-P1-MM3-001 →

Same trap: tangent-perpendicular-radius

P1MM3Level 2

TMUA-P1-MM3-009

A circle has centre O(0, 0) and the point P(6, 4) lies on it. Find the equation of the tangent to the circle at P.

Coordinate geometry in the (x,y)-plane

Open TMUA-P1-MM3-009 →

Step up a level

P1MM3Level 3

TMUA-P1-MM3-010

The line y = x + 1 crosses the circle x^2 + y^2 = 25 at two points. What is the length of the chord joining them?

Coordinate geometry in the (x,y)-plane

Open TMUA-P1-MM3-010 →

TMUA-P1X-MM3-03 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 2

Options

Keep practising

Master Coordinate geometry in the (x,y)-plane

TMUA-P1X-MM3-03 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 2

Options

Keep practising

Master Coordinate geometry in the (x,y)-plane