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The equation, \( \Large ax^{2}+2hxy+b^{2}+2gx+2fy+c=0 \) represents a circle if

A) \( \Large h^{2} = ab \)
B) \( \Large a = b \)
C) \( \Large h^{2}+ab = 0 \)
D) \( \Large a = b\ and\ h = 0 \)

Correct Answer:




D) \( \Large a = b\ and\ h = 0 \)

Description for Correct answer:
The given equation is \( \Large ax^{2}+2hxy+by^{2}+2gx+2fy+c=0 \) putting a = b and h = 0 we get general equation of circle

\( \Large x^{2}+y^{2}+2gx+2fy+c=0 \)

Part of solved Loci and concurrency questions and answers : >> Elementary Mathematics >> Loci and concurrency

Comments

Similar Questions

1). Consider following statements relating to the chords and arcs of a circle :
1. Equal chords are equidistant from the centre.
2. Between two arcs, the one that subtends a larger angle at the centre is larger.
3. If two arcs are of the same length, so are the chords joining their extremities.
Of these statements :

A). 1 and 2 are correct

B). 2 and 3 are correct

C). 1 and 3 are correct

D). 1, 2 and 3 are correct

2). Sum of the diamters of two circles is 35 cm and difference of their circumferences is 22 cm. Then area of the smaller circle will be

A). 121 sq. cm

B). 144 sq. m

C). 154 sq. cm

D). 308 sq. m

3). The area of the given figure is

A). \( \Large \frac{3}{4} \pi r^{2} \)

B). \( \Large \frac{1}{4} \pi r^{2} \)

C). \( \Large \pi r^{2} \)

D). \( \Large 3 \pi r^{2} \)

4). Chords AB and CD of a circle intersect at O. If AO = 8 cms, BO = 9 cms and CO = 2 DO, then length of DO (in cms) is

A). 5.67 approx.

B). 5

C). 6

D). 6.17 (approx)

5). If A, B be points of contact of the tangents drawn to a circle C with centre O and radius r cm from a point P Outside C, then which one of the following is correct ?

A). If M is mid-point of AB, then OM + MP > OP.

B). If M is mid-point of AB, then AMP is an acute angled triangle.

C). If M is mid-point of AB, then AM is perpendicular to OP.

D). Either \( \Large \triangle AOP \) is obtuse-angled or \( \Large \triangle BOP \) is obtuse-angled.

6). If C be a circle with centre O and radius 5 cm, then locus of mid-points of equal chords of C each of length 6 cm is a

A). concentric circle whose radius is 7 cm.

B). concentric circle whose radius is 4 cm.

C). straight line parallel to some chord of length of 6 cm.

D). straight line perpendicular to some chord of length of 6 cm.

7). If area of circle is 13.86 hectares, then cost of fencing it at the rate of 60 paise per metre is

A). Rs.784.00

B). Rs.788.00

C). Rs.792.00

D). Rs.796.00

8). If chords AP and AQ of a circle of radius 6 cm are at distance 3 cm and \( \Large 3\sqrt{2} \) cm respectively from the centre O of the circle, then area of the smaller sector POQ is

A). \( \Large 24 \pi cm^{2} \)

B). \( \Large 21 \pi cm^{2} \)

C). \( \Large 15 \pi cm^{2} \)

D). \( \Large 12 \pi cm^{2} \)

9). If C be a circle with centre O and radius x cm, then locus of midpoints of equal chords of C each of length y cm will be

A). a circle with centre O and radius \( \Large \frac{1}{2}\sqrt{4x^{2}+y^{2}} cm \)

B). a circle with centre O and radius \( \Large \frac{1}{2}\sqrt{4x^{2}-y^{2}} cm \)

C). diameter of the circle C

D). a circle with centre O and radius \( \Large \frac{1}{2}\sqrt{4x^{2}-x^{2}} cm \)

10). The straight lines AB and CD intersect at E. If EF and EG are bisectors of \( \Large \angle DEA\ and\ \angle AEC \) respectively and if \( \Large \angle AEF = x\ and\ \angle AEG = y \), then

A). \( \Large x + y > 90 ^{\circ} \)

B). \( \Large x + y < 90 ^{\circ} \)

C). \( \Large x + y = 90 ^{\circ} \)

D). \( \Large x + y = 180 ^{\circ} \)