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PSLE

PSLE Foundation Mathematics

<p>The line $y + 3x = 6$ intersects the circle, $C_{1}$, $x^{2} + y^{2} - 2x - 4y = 11$ at $A$ and $B$.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">State the centre and find the radius of the circle.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the coordinates of $A$ and $B$ and state if&nbsp;$AB$ is the diameter of the circle.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the equation of the circle $C_{2}$, when&nbsp;$C_{1}$ is reflected along the line $x = 3$.</span></div></li></ol>

The line $y + 3x = 6$ intersects the circle, $C_{1}$, $x^{2} + y^{2} - 2x - 4y = 11$ at $A$ and $B$.

State the centre and find the radius of the circle.

Find the coordinates of $A$ and $B$ and state if $AB$ is the diameter of the circle.

Find the equation of the circle $C_{2}$, when $C_{1}$ is reflected along the line $x = 3$.

Finding the Centre and Radius of a Circle

Finding the Equation of a Circle

Reflections and Translations of Circles

Line–Circle Intersections

Coordinate Geometry

<p>The points $A(7, 7)$ and $B(-2, -5)$ are at the opposite ends of a diameter of a circle $C_1$. Find the</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">centre of the circle and the radius of the circle.</span></div></li><li><div class="list-item-content"><span class="list-item-text">equation of the circle.</span></div></li><li><div class="list-item-content"><span class="list-item-text">equation of the perpendicular bisector $AB$.</span></div></li></ol>
<p>The circle, $C_1$, is reflected in the $x$-axis.</p>
<ol class="abc-list" start="4"><li><div class="list-item-content"><span class="list-item-text">Find the equation of the reflected circle, $C_2$.</span></div></li></ol>

The points $A(7, 7)$ and $B(-2, -5)$ are at the opposite ends of a diameter of a circle $C_1$. Find the

centre of the circle and the radius of the circle.

equation of the perpendicular bisector $AB$.

The circle, $C_1$, is reflected in the $x$-axis.

Find the equation of the reflected circle, $C_2$.

Perpendicular Bisectors

<p>The line $y+2x=5$ intersects the circle, ${{C}_{1}}$, ${{x}^{2}}+{{y}^{2}}-4x-6y=12$ at $A$ and $B$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">State the centre of the circle and find the radius of the circle.</div></li><li><div class="list-item-paragraph">Given that the coordinates of $A$ and $B$ are $\left( -1,7 \right)$ and $\left( \frac{17}{5},-\frac{9}{5} \right)$ respectively, show that&nbsp;$AB$ is not a diameter of the circle.</div></li><li><div class="list-item-paragraph">Find the equation of the circle, ${{C}_{2}}$, when&nbsp;${{C}_{1}}$ is reflected along the line $x=1$.</div></li></ol>

The line $y+2x=5$ intersects the circle, ${{C}_{1}}$, ${{x}^{2}}+{{y}^{2}}-4x-6y=12$ at $A$ and $B$.

Length of a Line Segment

<p>The equation of the circle ${{C}_{1}}$ is given by ${{x}^{2}}+{{y}^{2}}-10x+6y+30=0$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the coordinates of its center and the length of its radius.</div></li><li><div class="list-item-paragraph">Show that the circle ${{C}_{1}}$ touches the line $x=3$.</div></li><li><div class="list-item-paragraph">The circle, ${{C}_{1}}$ is reflected about the line$x=1$. Find the equation of the reflected circle, ${{C}_{2}}$.</div></li><li><div class="list-item-paragraph">Find the equation of another circle ${{C}_{3}}$ which has an area that is $4$ times larger than ${{C}_{1}}$ and its center at the origin.</div></li></ol>

The equation of the circle ${{C}_{1}}$ is given by ${{x}^{2}}+{{y}^{2}}-10x+6y+30=0$.

Tangents and Normals to Circles

<p>The points $A\left( -2,4 \right)$ and $B\left( 6,-2 \right)$ are at the opposite ends of a diameter of a circle, ${{C}_{1}}$. Find the</p>
<ol class="abc-list"><li><div class="list-item-paragraph">centre of the circle and radius of the circle.</div></li><li><div class="list-item-paragraph">equation of the circle.</div></li><li><div class="list-item-paragraph">equation of the perpendicular bisector of $AB$.</div></li></ol>
<p>The circle, ${{C}_{1}}$, is reflected in the $x$-axis.</p>
<ol class="abc-list" start="4"><li><div class="list-item-paragraph">Find the equation of the reflected circle, ${{C}_{2}}$.</div></li></ol>

The points $A\left( -2,4 \right)$ and $B\left( 6,-2 \right)$ are at the opposite ends of a diameter of a circle, ${{C}_{1}}$. Find the

The circle, ${{C}_{1}}$, is reflected in the $x$-axis.

Math Question Bank